# zbMATH — the first resource for mathematics

## Set-Valued and Variational Analysis

### Theory and Applications

 Short Title: Set-Valued Var. Anal. Publisher: Springer Netherlands, Dordrecht ISSN: 1877-0533; 1877-0541/e Online: http://link.springer.com/journal/volumesAndIssues/11228 Predecessor: Set-Valued Analysis Comments: Indexed cover-to-cover
 Documents Indexed: 468 Publications (since 2009) References Indexed: 453 Publications with 13,179 References.
all top 5

#### Latest Issues

 29, No. 3 (2021) 29, No. 2 (2021) 29, No. 1 (2021) 28, No. 4 (2020) 28, No. 3 (2020) 28, No. 2 (2020) 28, No. 1 (2020) 27, No. 4 (2019) 27, No. 3 (2019) 27, No. 2 (2019) 27, No. 1 (2019) 26, No. 4 (2018) 26, No. 3 (2018) 26, No. 2 (2018) 26, No. 1 (2018) 25, No. 4 (2017) 25, No. 3 (2017) 25, No. 2 (2017) 25, No. 1 (2017) 24, No. 4 (2016) 24, No. 3 (2016) 24, No. 2 (2016) 24, No. 1 (2016) 23, No. 4 (2015) 23, No. 3 (2015) 23, No. 2 (2015) 23, No. 1 (2015) 22, No. 4 (2014) 22, No. 3 (2014) 22, No. 2 (2014) 22, No. 1 (2014) 21, No. 4 (2013) 21, No. 3 (2013) 21, No. 2 (2013) 21, No. 1 (2013) 20, No. 4 (2012) 20, No. 3 (2012) 20, No. 2 (2012) 20, No. 1 (2012) 19, No. 4 (2011) 19, No. 3 (2011) 19, No. 2 (2011) 19, No. 1 (2011) 18, No. 3-4 (2010) 18, No. 2 (2010) 18, No. 1 (2010) 17, No. 4 (2009) 17, No. 3 (2009) 17, No. 2 (2009) 17, No. 1 (2009)
all top 5

#### Authors

 11 Mordukhovich, Boris S. 10 Bauschke, Heinz H. 10 López-Cerdá, Marco Antonio 10 Outrata, Jiří V. 10 Zaslavski, Alexander Yakovlevich 9 Wang, Shawn Xianfu 8 Henrion, René 8 Kruger, Alexander Ya. 8 Théra, Michel A. 8 Zhang, Liwei 7 Adly, Samir 7 Burachik, Regina Sandra 7 Gfrerer, Helmut 6 Borwein, Jonathan Michael 6 Boţ, Radu Ioan 6 Combettes, Patrick L. 6 Goberna, Miguel Angel 6 Hantoute, Abderrahim 6 Martínez-Legaz, Juan-Enrique 6 Thibault, Lionel 5 Beer, Gerald Alan 5 de Pinho, Maria do Rosário 5 Nam, Nguyen Mau 5 Reich, Simeon 5 Seeger, Alberto 5 Simons, Stephen 5 Valero, José 5 Volle, Michel 5 Yao, Jen-Chih 5 Ye, Jane J. 4 Arutyunov, Aram Vladimirovic 4 Bianchi, Monica 4 Bounkhel, Messaoud 4 Cánovas, María Josefa 4 Castaing, Charles 4 Csetnek, Ernö Robert 4 Dontchev, Asen L. 4 Eberhard, Andrew C. 4 Fabian, Marián J. 4 Li, Shengjie 4 Luke, D. Russell 4 Penot, Jean-Paul 4 Pini, Rita 4 Smirnov, Georgi V. 4 Uderzo, Amos 4 Wachsmuth, Gerd 4 Yao, Liangjin 4 Zhukovskiĭ, Sergeĭ Evgen’evich 3 Aragón Artacho, Francisco Javier 3 Attouch, Hedy 3 Aussel, Didier 3 Azzam-Laouir, Dalila 3 Červinka, Michal 3 Cibulka, Radek 3 Colombo, Giovanni 3 Correa, Rafael 3 Daniilidis, Aris 3 Donchev, Tzanko Donchev 3 Durea, Marius 3 Huang, Hui 3 Huynh Van Ngai 3 Ivanov, Grigorii E. 3 Kassay, Gábor 3 Konnov, Igor V. 3 Lassonde, Marc 3 Le, Ba Khiet 3 Mehlitz, Patrick 3 Meng, Kaiwen 3 Movahedian, Nooshin 3 Noll, Dominikus 3 Pang, Liping 3 Parra, Juan 3 Phan, Hung M. 3 Pištěk, Miroslav 3 Roberto, Lucchetti E. 3 Rockafellar, Ralph Tyrrell 3 Royset, Johannes O. 3 Sagara, Nobusumi 3 Sagastizábal, Claudia A. 3 Sagastizábal, Claudia S. 3 Shanbhag, Uday V. 3 Soubeyran, Antoine 3 Strugariu, Radu 3 Toledo, Fco. Javier 3 Van Ackooij, Wim 3 Voisei, Mircea Dan 3 Wang, Bingwu 3 Wu, Jia 3 Yang, Xiaoqi 3 Zhang, Yi 3 Zidani, Hasnaa 2 Adam, Lukáš 2 Apkarian, Pierre 2 Aronna, María Soledad 2 Benedetti, Irene 2 Benko, Matus 2 Bento, Glaydston C. 2 Bonnans, Joseph Frédéric 2 Bueno, Orestes 2 Burke, James V. ...and 490 more Authors
all top 5

#### Fields

 277 Calculus of variations and optimal control; optimization (49-XX) 201 Operations research, mathematical programming (90-XX) 112 Operator theory (47-XX) 60 Functional analysis (46-XX) 58 Ordinary differential equations (34-XX) 51 Numerical analysis (65-XX) 40 General topology (54-XX) 39 Real functions (26-XX) 32 Partial differential equations (35-XX) 28 Global analysis, analysis on manifolds (58-XX) 27 Convex and discrete geometry (52-XX) 24 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 23 Measure and integration (28-XX) 23 Systems theory; control (93-XX) 19 Dynamical systems and ergodic theory (37-XX) 12 General and overarching topics; collections (00-XX) 9 Approximations and expansions (41-XX) 8 History and biography (01-XX) 8 Probability theory and stochastic processes (60-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 6 Difference and functional equations (39-XX) 5 Computer science (68-XX) 4 Mechanics of deformable solids (74-XX) 3 Mathematical logic and foundations (03-XX) 3 Information and communication theory, circuits (94-XX) 2 Topological groups, Lie groups (22-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Biology and other natural sciences (92-XX) 1 Special functions (33-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Mechanics of particles and systems (70-XX)

#### Citations contained in zbMATH Open

351 Publications have been cited 2,160 times in 1,717 Documents Cited by Year
Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators. Zbl 1284.47043
Combettes, Patrick L.; Pesquet, Jean-Christophe
2012
Error bounds: necessary and sufficient conditions. Zbl 1192.49018
Fabian, Marian J.; Henrion, René; Kruger, Alexander Y.; Outrata, Jiří V.
2010
A three-operator splitting scheme and its optimization applications. Zbl 1464.47041
Davis, Damek; Yin, Wotao
2017
On directional metric regularity, subregularity and optimality conditions for nonsmooth mathematical programs. Zbl 1321.49031
Gfrerer, Helmut
2013
Common solutions to variational inequalities. Zbl 1296.47060
Censor, Yair; Gibali, Aviv; Reich, Simeon; Sabach, Shoham
2012
A duality theory for set-valued functions. I: Fenchel conjugation theory. Zbl 1168.49031
Hamel, Andreas H.
2009
Iterative methods for generalized split feasibility problems in Hilbert spaces. Zbl 1326.47099
Takahashi, Wataru; Xu, Hong-Kun; Yao, Jen-Chin
2015
Multiple solutions for nonlinear coercive problems with a nonhomogeneous differential operator and a nonsmooth potential. Zbl 1258.35075
Gasiński, Leszek; Papageorgiou, Nikolaos S.
2012
Restricted normal cones and the method of alternating projections: theory. Zbl 1272.49027
Bauschke, Heinz H.; Luke, D. Russell; Phan, Hung M.; Wang, Xianfu
2013
Resolvents of set-valued monotone vector fields in Hadamard manifolds. Zbl 1239.47043
Li, Chong; López, Genaro; Martín-Márquez, Victoria; Wang, Jin-Hua
2011
Generic existence and approximation of fixed points for nonexpansive set-valued maps. Zbl 1183.47055
de Blasi, Francesco S.; Myjak, Józef; Reich, Simeon; Zaslavski, Alexander J.
2009
Dualization of signal recovery problems. Zbl 1229.90123
Combettes, Patrick L.; Dũng, Đinh; Vũ, Băng Công
2010
Forward-backward and Tseng’s type penalty schemes for monotone inclusion problems. Zbl 1308.47064
Boţ, Radu Ioan; Csetnek, Ernö Robert
2014
Error bounds and Hölder metric subregularity. Zbl 1330.49012
Kruger, Alexander Y.
2015
A second-order model for image denoising. Zbl 1203.94006
Bergounioux, Maïtine; Piffet, Loic
2010
Robust duality in parametric convex optimization. Zbl 1327.90195
Boţ, R. I.; Jeyakumar, V.; Li, G. Y.
2013
First and second order convex sweeping processes in reflexive smooth Banach spaces. Zbl 1200.34067
Bounkhel, Messaoud; Al-Yusof, Rabab
2010
Firmly nonexpansive mappings and maximally monotone operators: correspondence and duality. Zbl 1263.47066
Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu
2012
Calculus rules for derivatives of multimaps. Zbl 1173.54008
Li, S. J.; Meng, K. W.; Penot, J.-P.
2009
Discrete approximations of a controlled sweeping process. Zbl 1312.49015
Colombo, G.; Henrion, R.; Hoang, N. D.; Mordukhovich, B. S.
2015
Restricted normal cones and the method of alternating projections: applications. Zbl 1349.65191
Bauschke, Heinz H.; Luke, D. Russell; Phan, Hung M.; Wang, Xianfu
2013
Regularity of weak solutions and their attractors for a parabolic feedback control problem. Zbl 1327.35468
Kasyanov, Pavlo O.; Toscano, Luisa; Zadoianchuk, Nina V.
2013
On subregularity properties of set-valued mappings. Zbl 1285.90062
Apetrii, Marius; Durea, Marius; Strugariu, Radu
2013
Codifferential calculus. Zbl 1262.47074
Li, Shengjie; Penot, Jean-Paul; Xue, Xiaowei
2011
On global attractors of multivalued semiflows generated by the 3D Bénard system. Zbl 1259.35042
Kapustyan, Alexey V.; Pankov, Andrey V.; Valero, José
2012
On metric pseudo-(sub)regularity of multifunctions and optimality conditions for degenerated mathematical programs. Zbl 1297.49023
Gfrerer, Helmut
2014
About subtransversality of collections of sets. Zbl 1383.49028
Kruger, Alexander Y.; Luke, D. Russell; Thao, Nguyen H.
2017
Variational analysis of directional minimal time functions and applications to location problems. Zbl 1321.49028
Nam, Nguyen Mau; Zălinescu, Constantin
2013
A maximum principle for the controlled sweeping process. Zbl 1398.49015
Arroud, Chems Eddine; Colombo, Giovanni
2018
Generalized control systems in the space of probability measures. Zbl 1400.93330
Cavagnari, Giulia; Marigonda, Antonio; Nguyen, Khai T.; Priuli, Fabio S.
2018
Calmness of the feasible set mapping for linear inequality systems. Zbl 1297.90163
Cánovas, M. J.; López, M. A.; Parra, J.; Toledo, F. J.
2014
A proximal point-type method for multicriteria optimization. Zbl 1296.90113
Bento, G. C.; Neto, J. X. Cruz; Soubeyran, A.
2014
Inradius and circumradius of various convex cones arising in applications. Zbl 1217.46047
Henrion, René; Seeger, Alberto
2010
On properties of different notions of centers for convex cones. Zbl 1198.46011
Henrion, René; Seeger, Alberto
2010
Convergence properties of a smoothing approach for mathematical programs with second-order cone complementarity constraints. Zbl 1261.90058
Zhang, Yi; Zhang, Liwei; Wu, Jia
2011
Clarke generalized Jacobian of the projection onto symmetric cones. Zbl 1168.49043
Kong, Lingchen; Tunçel, Levent; Xiu, Naihua
2009
Asymptotics for some proximal-like method involving inertia and memory aspects. Zbl 1214.65037
Cabot, Alexandre; Frankel, Pierre
2011
Graphical derivatives and stability analysis for parameterized equilibria with conic constraints. Zbl 1330.49013
Mordukhovich, Boris S.; Outrata, Jiri V.; Ramírez C., Héctor
2015
Cutting plane oracles to minimize non-smooth non-convex functions. Zbl 1219.49013
Noll, Dominikus
2010
A shared-constraint approach to multi-leader multi-follower games. Zbl 1307.91046
Kulkarni, Ankur A.; Shanbhag, Uday V.
2014
Local search proximal algorithms as decision dynamics with costs to move. Zbl 1209.49042
Attouch, H.; Soubeyran, A.
2011
On the theory of global attractors and Lyapunov functionals. Zbl 1260.37048
Coti Zelati, Michele
2013
Uniform continuity, uniform convergence, and shields. Zbl 1236.54012
Beer, Gerald; Levi, Sandro
2010
Flow invariance on stratified domains. Zbl 1327.93215
Barnard, Richard C.; Wolenski, Peter R.
2013
On optimality conditions in control of elliptic variational inequalities. Zbl 1211.49036
Outrata, Jiří; Jarušek, Jiří; Stará, Jana
2011
Infimum gaps for limit solutions. Zbl 1311.49087
Aronna, M.-Soledad; Motta, Monica; Rampazzo, Franco
2015
Mathematical programs with semidefinite cone complementarity constraints: constraint qualifications and optimality conditions. Zbl 1296.90118
Wu, Jia; Zhang, Liwei; Zhang, Yi
2014
Mixed semicontinuous perturbation of nonconvex state-dependent sweeping process. Zbl 1307.34033
Azzam-Laouir, Dalila; Izza, Sabrina; Thibault, Lionel
2014
On proximal subgradient splitting method for minimizing the sum of two nonsmooth convex functions. Zbl 1365.65160
Bello Cruz, José Yunier
2017
Gradient consistency for integral-convolution smoothing functions. Zbl 1321.49027
Burke, James V.; Hoheisel, Tim; Kanzow, Christian
2013
Solving ill-posed bilevel programs. Zbl 1362.90346
Zemkoho, Alain B.
2016
On some regularity properties in variational analysis. Zbl 1177.49032
Uderzo, Amos
2009
Metric regularity of mappings and generalized normals to set images. Zbl 1218.49023
Mordukhovich, Boris S.; Nam, Nguyen Mau; Wang, Bingwu
2009
Three solutions for a partial differential inclusion via nonsmooth critical point theory. Zbl 1219.35381
Iannizzotto, Antonio
2011
Global solutions for nonlinear delay evolution inclusions with nonlocal initial conditions. Zbl 1266.34127
Vrabie, Ioan I.
2012
Infinite horizon optimal control problems in the light of convex analysis in Hilbert spaces. Zbl 1311.49084
Pickenhain, Sabine
2015
Fixed points and variational principles with applications to capability theory of wellbeing via variational rationality. Zbl 1318.49029
Bao, T. Q.; Mordukhovich, B. S.; Soubeyran, A.
2015
About intrinsic transversality of pairs of sets. Zbl 1387.49023
Kruger, Alexander Y.
2018
Optimal control involving sweeping processes. Zbl 1419.49030
de Pinho, M. d. R.; Ferreira, M. M. A.; Smirnov, G. V.
2019
Negatively invariant sets and entire trajectories of set-valued dynamical systems. Zbl 1225.37022
Kloeden, Peter E.; Marín-Rubio, Pedro
2011
The Josephy-Newton method for semismooth generalized equations and semismooth SQP for optimization. Zbl 1285.90065
Izmailov, Alexey F.; Kurennoy, Alexey S.; Solodov, Mikhail V.
2013
Linear monotone subspaces of locally convex spaces. Zbl 1192.47047
Voisei, M. D.; Zălinescu, C.
2010
State dependent sweeping process in $$p$$-uniformly smooth and $$q$$-uniformly convex Banach spaces. Zbl 1262.34072
Bounkhel, Messaoud; Castaing, Charles
2012
Fixed points, fixed sets and iterated multifunction systems for nonself multivalued operators. Zbl 1328.54047
2015
Equivalent conditions for local error bounds. Zbl 1254.49011
Meng, K. W.; Yang, X. Q.
2012
Nonlocal problems for differential inclusions in Hilbert spaces. Zbl 1312.34097
Benedetti, I.; Loi, N. V.; Malaguti, L.
2014
Strong and weak solutions to second order differential inclusions governed by monotone operators. Zbl 1315.34067
2014
Well-posedness of minimal time problems with constant dynamics in Banach spaces. Zbl 1219.49014
Colombo, Giovanni; Goncharov, Vladimir V.; Mordukhovich, Boris S.
2010
New formulas for the Fenchel subdifferential of the conjugate function. Zbl 1205.26018
Correa, Rafael; Hantoute, Abderrahim
2010
Convex inequalities without constraint qualification nor closedness condition, and their applications in optimization. Zbl 1231.90381
Dinh, N.; Goberna, M. A.; López, M. A.; Volle, M.
2010
A class of generalized evolutionary problems driven by variational inequalities and fractional operators. Zbl 1441.47076
Migórski, Stanisław; Zeng, Shengda
2019
Finite convergence of the proximal point algorithm for variational inequality problems. Zbl 1321.49016
Matsushita, Shin-Ya; Xu, Li
2013
A characterization of the subdifferential of singular Gaussian distribution functions. Zbl 1327.90159
van Ackooij, Wim; Minoux, M.
2015
Dynamics of the Douglas-Rachford method for ellipses and $$p$$-spheres. Zbl 06913665
Borwein, Jonathan M.; Lindstrom, Scott B.; Sims, Brailey; Schneider, Anna; Skerritt, Matthew P.
2018
The limiting normal cone to pointwise defined sets in Lebesgue spaces. Zbl 1401.49018
Mehlitz, Patrick; Wachsmuth, Gerd
2018
Perturbed evolution problems with continuous bounded variation in time and applications. Zbl 1403.34046
Azzam-Laouir, Dalila; Castaing, Charles; Monteiro Marques, M. D. P.
2018
On stochastic mirror-prox algorithms for stochastic Cartesian variational inequalities: randomized block coordinate and optimal averaging schemes. Zbl 07002699
Yousefian, Farzad; Nedić, Angelia; Shanbhag, Uday V.
2018
Constraint qualifications for nonsmooth mathematical programs with equilibrium constraints. Zbl 1191.90070
Movahedian, N.; Nobakhtian, S.
2009
Pareto solutions of polyhedral-valued vector optimization problems in Banach spaces. Zbl 1177.49033
Zheng, Xi Yin
2009
Characterizing convexity of a function by its Fréchet and limiting second-order subdifferentials. Zbl 1209.49031
Chieu, N. H.; Chuong, T. D.; Yao, J.-C.; Yen, N. D.
2011
A metric version of Milyutin theorem. Zbl 1250.49020
Uderzo, Amos
2012
Multivariate epi-splines and evolving function identification problems. Zbl 1356.41004
Royset, Johannes O.; Wets, Roger J.-B.
2016
Stability and optimality of solutions to differential inclusions via averaging method. Zbl 1307.34001
Gama, Ricardo; Smirnov, Georgi
2014
Nonsmooth bundle trust-region algorithm with applications to robust stability. Zbl 1334.49092
Apkarian, Pierre; Noll, Dominikus; Ravanbod, Laleh
2016
Strong stationarity for optimization problems with complementarity constraints in absence of polyhedricity. With applications to optimization with semidefinite and second-order-cone complementarity constraints. Zbl 1368.49018
Wachsmuth, Gerd
2017
Second-order optimality conditions for a semilinear elliptic optimal control problem with mixed pointwise constraints. Zbl 1368.49023
Kien, B. T.; Nhu, V. H.; Son, N. H.
2017
Subgradients of the value function to a parametric optimal control problem. Zbl 1214.47064
Toan, N. T.; Kien, B. T.
2010
A generalized inexact proximal point method for nonsmooth functions that satisfies Kurdyka Łojasiewicz inequality. Zbl 1342.49019
Bento, Glaydston C.; Soubeyran, Antoine
2015
Attractors for multi-valued non-autonomous dynamical systems: relationship, characterization and robustness. Zbl 1401.37085
Cui, Hongyong; Langa, José A.; Li, Yangrong; Valero, José
2018
Any semitopological group that is homeomorphic to a product of Čech-complete spaces is a topological group. Zbl 1321.22006
Moors, Warren B.
2013
Necessary optimality conditions for optimal control problems with nonsmooth mixed state and control constraints. Zbl 1350.49027
Li, An; Ye, Jane J.
2016
Generalized topological essentiality and coincidence points of multivalued maps. Zbl 1182.54052
Gabor, Grzegorz; Górniewicz, Lech; Ślosarski, Mirosław
2009
An answer to S. Simons’ question on the maximal monotonicity of the sum of a maximal monotone linear operator and a normal cone operator. Zbl 1198.47070
Bauschke, Heinz H.; Wang, Xianfu; Yao, Liangjin
2009
Lower semicontinuity of the feasible set mapping of linear systems relative to their domains. Zbl 1257.49023
Daniilidis, Aris; Goberna, Miguel A.; López, Marco A.; Lucchetti, Roberto
2013
Value functions and transversality conditions for infinite-horizon optimal control problems. Zbl 1182.49021
Sagara, Nobusumi
2010
Affine nonexpansive operators, Attouch-Théra duality and the Douglas-Rachford algorithm. Zbl 06804490
Bauschke, Heinz H.; Lukens, Brett; Moursi, Walaa M.
2017
On the response of autonomous sweeping processes to periodic perturbations. Zbl 1362.34031
Kamenskii, Mikhail; Makarenkov, Oleg
2016
About semicontinuity of set-valued maps and stability of quasivariational inclusions. Zbl 1296.90120
Anh, Lam Quoc; Khanh, Phan Quoc; Quy, Dinh Ngoc
2014
Necessary optimality conditions for mathematical programs with second-order cone complementarity constraints. Zbl 1297.90152
Liang, Yan-Chao; Zhu, Xi-De; Lin, Gui-Hua
2014
Stability in linear optimization under perturbations of the left-hand side coefficients. Zbl 1330.49023
Daniilidis, A.; Goberna, M. A.; Lopez, M. A.; Lucchetti, R.
2015
New inertial factors of the Krasnosel’skiĭ-Mann iteration. Zbl 07345313
Dong, Yunda
2021
Resolvents and Yosida approximations of displacement mappings of isometries. Zbl 07383628
Alwadani, Salihah; Bauschke, Heinz H.; Revalski, Julian P.; Wang, Xianfu
2021
Deep neural network structures solving variational inequalities. Zbl 1448.49014
Combettes, Patrick L.; Pesquet, Jean-Christophe
2020
Metric regularity of quasidifferentiable mappings and optimality conditions for nonsmooth mathematical programming problems. Zbl 07243969
Dolgopolik, M. V.
2020
Duality for the robust sum of functions. Zbl 07193689
Dinh, N.; Goberna, M. A.; Volle, Michel
2020
Some results on strongly pseudomonotone quasi-variational inequalities. Zbl 1441.49013
Nguyen, Luong V.; Qin, Xiaolong
2020
Generalized derivatives for the solution operator of the obstacle problem. Zbl 1442.49030
Rauls, Anne-Therese; Wachsmuth, Gerd
2020
On inexact relative-error hybrid proximal extragradient, forward-backward and Tseng’s modified forward-backward methods with inertial effects. Zbl 1445.90079
Alves, M. Marques; Marcavillaca, Raul T.
2020
The radius of metric subregularity. Zbl 1447.49030
Dontchev, Asen L.; Gfrerer, Helmut; Kruger, Alexander Y.; Outrata, Jiří V.
2020
Continuous dynamics related to monotone inclusions and non-smooth optimization problems. Zbl 07344788
Csetnek, Ernö Robert
2020
Some new characterizations of intrinsic transversality in Hilbert spaces. Zbl 1437.90152
Thao, Nguyen Hieu; Bui, Hoa T.; Cuong, Nguyen Duy; Verhaegen, Michel
2020
Directional metric pseudo subregularity of set-valued mappings: a general model. Zbl 1439.49028
Van Ngai, Huynh; Tron, Nguyen Huu; Van Vu, Nguyen; Théra, Michel
2020
Bartle-Graves theorem revisited. Zbl 1444.47068
Dontchev, Asen L.
2020
Finite alternation theorems and a constructive approach to piecewise polynomial approximation in Chebyshev norm. Zbl 1444.41004
Crouzeix, Jean-Pierre; Sukhorukova, Nadezda; Ugon, Julien
2020
Stability analysis for parameterized variational systems with implicit constraints. Zbl 1437.49017
Benko, Matúš; Gfrerer, Helmut; Outrata, Jiří V.
2020
An inverse mapping theorem in Fréchet-Montel spaces. Zbl 1446.49014
Cibulka, Radek; Fabian, Marián; Roubal, Tomáš
2020
The $$\mathcal{U}$$-Lagrangian, fast track, and partial smoothness of a prox-regular function. Zbl 1441.49020
Liu, Shuai; Eberhard, Andrew; Luo, Yousong
2020
Epi/hypo-convergence of bifunctions on general domains and approximations of quasi-variational problems. Zbl 1450.90052
Diem, H. T. H.; Khanh, P. Q.
2020
Evolution inclusions governed by time-dependent maximal monotone operators with a full domain. Zbl 07243976
Vilches, Emilio; Nguyen, Bao Tran
2020
Nonsmoothness in machine learning: specific structure, proximal identification, and applications. Zbl 07344790
Iutzeler, Franck; Malick, Jérôme
2020
Optimal control involving sweeping processes. Zbl 1419.49030
de Pinho, M. d. R.; Ferreira, M. M. A.; Smirnov, G. V.
2019
A class of generalized evolutionary problems driven by variational inequalities and fractional operators. Zbl 1441.47076
Migórski, Stanisław; Zeng, Shengda
2019
An inertial algorithm for DC programming. Zbl 1434.90151
de Oliveira, Welington; Tcheou, Michel P.
2019
Sensitivity analysis for a class of $$H_{0}^{1}$$-elliptic variational inequalities of the second kind. Zbl 1416.35036
Christof, Constantin; Meyer, Christian
2019
Dissipative and non-dissipative evolutionary quasi-variational inequalities with gradient constraints. Zbl 1418.35248
Hintermüller, M.; Rautenberg, C. N.; Strogies, N.
2019
Calculus for directional limiting normal cones and subdifferentials. Zbl 1426.49018
Benko, Matúš; Gfrerer, Helmut; Outrata, Jiří V.
2019
Inversion of nonsmooth maps between Banach spaces. Zbl 1433.49021
Jaramillo, Jesús A.; Lajara, Sebastián; Madiedo, Óscar
2019
Connectedness of approximate efficient solutions for generalized semi-infinite vector optimization problems. Zbl 1430.90514
Peng, Zai-Yun; Wang, Xianfu; Yang, Xin-Min
2019
On a method of solving some functional equations for set-valued functions. Zbl 1428.39032
Sikorska, Justyna
2019
Metric regularity properties in bang-bang type linear-quadratic optimal control problems. Zbl 1419.49012
Preininger, J.; Scarinci, T.; Veliov, V. M.
2019
Convergence analysis of the implicit Euler-discretization and sufficient conditions for optimal control problems subject to index-one differential-algebraic equations. Zbl 1419.49007
Martens, Björn; Gerdts, Matthias
2019
About asymptotic analysis and set optimization. Zbl 07115100
Hernández, Elvira; López, Rubén
2019
On the sequential normal compactness condition and its restrictiveness in selected function spaces. Zbl 1428.49019
Mehlitz, Patrick
2019
Linearized M-stationarity conditions for general optimization problems. Zbl 1430.90556
Gfrerer, Helmut
2019
Theorems of the alternative for systems of convex inequalities. Zbl 07058435
Arutyunov, Aram V.; Zhukovskiy, Sergey E.; Marinkovic, Boban
2019
Regular and limiting normal cones to the graph of the subdifferential mapping of the nuclear norm. Zbl 1416.49018
Liu, Yulan; Pan, Shaohua
2019
Analysis of optimal control problems of semilinear elliptic equations by BV-functions. Zbl 1421.35124
Casas, Eduardo; Kunisch, Karl
2019
Lyapunov pairs in semilinear differential problems with state-dependent impulses. Zbl 1426.34074
Benedetti, I.; Cardinali, T.; Gabor, G.; Rubbioni, P.
2019
Computation of the epsilon-subdifferential of convex piecewise linear-quadratic functions in optimal worst-case time. Zbl 07115099
Kumar, Deepak; Lucet, Yves
2019
New constraint qualifications and optimality conditions for second order cone programs. Zbl 1423.90249
Zhang, Yi; Zhang, Liwei
2019
Variations of deformations with self-contact on Lipschitz domains. Zbl 1431.35200
Palmer, Aaron Zeff
2019
Well-posedness and subdifferentials of optimal value and infimal convolution. Zbl 1430.49009
Ivanov, Grigorii E.; Thibault, Lionel
2019
Progressive decoupling of linkages in optimization and variational inequalities with elicitable convexity or monotonicity. Zbl 07146007
Rockafellar, R. Tyrrell
2019
Hölder error bounds and Hölder calmness with applications to convex semi-infinite optimization. Zbl 1430.49014
Kruger, Alexander Y.; López, Marco A.; Yang, Xiaoqi; Zhu, Jiangxing
2019
Correction to: Optimal control involving sweeping processes. Zbl 1453.49012
de Pinho, M. d. R.; Ferreira, M. M. A.; Smirnov, G. V.
2019
On maximality of quasimonotone operators. Zbl 07058437
Bueno, Orestes; Cotrina, John
2019
Selective bi-coordinate method for limit non-smooth resource allocation type problems. Zbl 1420.90067
Konnov, I. V.
2019
Continuity of the metric projection and local solar properties of sets. Continuity of the metric projection and local solar properties of sets, continuity of the metric projection and solar properties. Zbl 1423.41050
Alimov, A. R.
2019
Trajectories of differential inclusions on Riemannian manifolds and invariance. Zbl 1417.58007
2019
The weak sequential closure of decomposable sets in Lebesgue spaces and its application to variational geometry. Zbl 1415.49014
Mehlitz, Patrick; Wachsmuth, Gerd
2019
Infinite horizon problems in the calculus of variations. The role of transformations with an application to the brachistochrone problem. Zbl 1419.49018
Pickenhain, Sabine
2019
Sensitivity properties of parametric nonconvex evolution inclusions with application to optimal control problems. Zbl 1421.49002
2019
Existence and Lyapunov pairs for the perturbed sweeping process governed by a fixed set. Zbl 1432.34081
Vilches, Emilio
2019
A maximum principle for the controlled sweeping process. Zbl 1398.49015
Arroud, Chems Eddine; Colombo, Giovanni
2018
Generalized control systems in the space of probability measures. Zbl 1400.93330
Cavagnari, Giulia; Marigonda, Antonio; Nguyen, Khai T.; Priuli, Fabio S.
2018
About intrinsic transversality of pairs of sets. Zbl 1387.49023
Kruger, Alexander Y.
2018
Dynamics of the Douglas-Rachford method for ellipses and $$p$$-spheres. Zbl 06913665
Borwein, Jonathan M.; Lindstrom, Scott B.; Sims, Brailey; Schneider, Anna; Skerritt, Matthew P.
2018
The limiting normal cone to pointwise defined sets in Lebesgue spaces. Zbl 1401.49018
Mehlitz, Patrick; Wachsmuth, Gerd
2018
Perturbed evolution problems with continuous bounded variation in time and applications. Zbl 1403.34046
Azzam-Laouir, Dalila; Castaing, Charles; Monteiro Marques, M. D. P.
2018
On stochastic mirror-prox algorithms for stochastic Cartesian variational inequalities: randomized block coordinate and optimal averaging schemes. Zbl 07002699
Yousefian, Farzad; Nedić, Angelia; Shanbhag, Uday V.
2018
Attractors for multi-valued non-autonomous dynamical systems: relationship, characterization and robustness. Zbl 1401.37085
Cui, Hongyong; Langa, José A.; Li, Yangrong; Valero, José
2018
Uniform continuity and a new bornology for a metric space. Zbl 1422.54019
Beer, Gerald; Garrido, M. Isabel; Meroño, Ana S.
2018
Equilibrium problems: existence results and applications. Zbl 06861473
Cotrina, John; García, Yboon
2018
Properties of chance constraints in infinite dimensions with an application to PDE constrained optimization. Zbl 1410.90135
Farshbaf-Shaker, M. H.; Henrion, R.; Hömberg, D.
2018
(Sub-)differentiability of probability functions with elliptical distributions. Zbl 1416.90028
van Ackooij, W.; Aleksovska, I.; Munoz-Zuniga, M.
2018
On the directional differentiability of the solution mapping for a class of variational inequalities of the second kind. Zbl 06936446
Hintermüller, M.; Surowiec, T. M.
2018
Solving stochastic programming problems with risk measures by progressive hedging. Zbl 1416.90027
Rockafellar, R. Tyrrell
2018
Solving graph coloring problems with the Douglas-Rachford algorithm. Zbl 06913660
Aragón Artacho, Francisco J.; Campoy, Rubén
2018
The Mayer and minimum time problems with stratified state constraints. Zbl 1404.35469
Hermosilla, C.; Wolenski, P. R.; Zidani, H.
2018
Viability theorem for deterministic mean field type control systems. Zbl 1406.49052
Averboukh, Yurii
2018
Perspective functions: properties, constructions, and examples. Zbl 1396.26021
Combettes, Patrick L.
2018
Full stability of general parametric variational systems. Zbl 1406.49011
Mordukhovich, B. S.; Nghia, T. T. A.; Pham, D. T.
2018
A partial answer to the Demyanov-Ryabova conjecture. Zbl 1387.52025
Daniilidis, Aris; Petitjean, Colin
2018
Necessary optimality conditions for implicit control systems with applications to control of differential algebraic equations. Zbl 1390.49018
Li, An; Ye, Jane J.
2018
A remark on the convergence of the Douglas-Rachford iteration in a non-convex setting. Zbl 06913656
2018
Stability of possibly nonisolated solutions of constrained equations, with applications to complementarity and equilibrium problems. Zbl 06913662
Arutyunov, A. V.; Izmailov, A. F.
2018
Computing proximal points of convex functions with inexact subgradients. Zbl 1401.49039
Hare, W.; Planiden, C.
2018
A review on ambiguity in stochastic portfolio optimization. Zbl 1416.90026
Pflug, Georg Ch.; Pohl, Mathias
2018
Upper semismooth functions and the subdifferential determination property. Zbl 1387.49021
Lassonde, Marc
2018
Approaching nonsmooth nonconvex optimization problems through first order dynamical systems with hidden acceleration and Hessian driven damping terms. Zbl 1452.90250
Boţ, Radu Ioan; Csetnek, Ernö Robert
2018
Symbolic computation with monotone operators. Zbl 06913663
Lauster, Florian; Luke, D. Russell; Tam, Matthew K.
2018
On second-order proto-differentiability of perturbation maps. Zbl 1395.90238
Tung, L. T.
2018
Quasidense monotone multifunctions. Zbl 06861465
Simons, Stephen
2018
Nearly Chebyshev sets are almost convex. Zbl 1387.41014
Moors, Warren B.
2018
SOS-convex semialgebraic programs and its applications to robust optimization: a tractable class of nonsmooth convex optimization. Zbl 1393.90083
Chieu, N. H.; Feng, J. W.; Gao, W.; Li, G.; Wu, D.
2018
On Bregman-type distances for convex functions and maximally monotone operators. Zbl 06913664
Burachik, Regina S.; Martínez-Legaz, Juan E.
2018
Non-smooth optimization for robust control of infinite-dimensional systems. Zbl 1393.90138
Apkarian, Pierre; Noll, Dominikus; Ravanbod, Laleh
2018
Algorithmic construction of the subdifferential from directional derivatives. Zbl 1403.52009
Audet, Charles; Hare, Warren
2018
Infimal convolution and optimal time control problem. I: Fréchet and proximal subdifferentials. Zbl 1400.49015
Ivanov, Grigorii E.; Thibault, Lionel
2018
The metric integral of set-valued functions. Zbl 1405.26030
Dyn, Nira; Farkhi, Elza; Mokhov, Alona
2018
Variance-optimal martingale measures for diffusion processes with stochastic coefficients. Zbl 1405.60056
Hernández-Hernández, Daniel
2018
Subgradient projectors: extensions, theory, and characterizations. Zbl 1422.49014
Bauschke, Heinz H.; Wang, Caifang; Wang, Xianfu; Xu, Jia
2018
A three-operator splitting scheme and its optimization applications. Zbl 1464.47041
Davis, Damek; Yin, Wotao
2017
About subtransversality of collections of sets. Zbl 1383.49028
Kruger, Alexander Y.; Luke, D. Russell; Thao, Nguyen H.
2017
On proximal subgradient splitting method for minimizing the sum of two nonsmooth convex functions. Zbl 1365.65160
Bello Cruz, José Yunier
2017
Strong stationarity for optimization problems with complementarity constraints in absence of polyhedricity. With applications to optimization with semidefinite and second-order-cone complementarity constraints. Zbl 1368.49018
Wachsmuth, Gerd
2017
Second-order optimality conditions for a semilinear elliptic optimal control problem with mixed pointwise constraints. Zbl 1368.49023
Kien, B. T.; Nhu, V. H.; Son, N. H.
2017
Affine nonexpansive operators, Attouch-Théra duality and the Douglas-Rachford algorithm. Zbl 06804490
Bauschke, Heinz H.; Lukens, Brett; Moursi, Walaa M.
2017
Stability of metric regularity with set-valued perturbations and application to Newton’s method for solving generalized equations. Zbl 1393.49012
Adly, Samir; Huynh Van Ngai; Nguyen Van Vu
2017
Stability of saddle points via explicit coderivatives of pointwise subdifferentials. Zbl 1367.49011
Clason, Christian; Valkonen, Tuomo
2017
...and 251 more Documents
all top 5

#### Cited by 1,804 Authors

 31 Boţ, Radu Ioan 23 Papageorgiou, Nikolaos S. 22 Kruger, Alexander Ya. 22 Mordukhovich, Boris S. 21 Csetnek, Ernö Robert 20 Bauschke, Heinz H. 20 Yao, Jen-Chih 19 Wang, Shawn Xianfu 17 Durea, Marius 17 Soubeyran, Antoine 17 Zaslavski, Alexander Yakovlevich 16 Zhang, Liwei 15 Hantoute, Abderrahim 15 López-Cerdá, Marco Antonio 15 Noll, Dominikus 14 Adly, Samir 14 Arutyunov, Aram Vladimirovic 14 Combettes, Patrick L. 14 Gfrerer, Helmut 14 Kasyanov, Pavlo O. 14 Strugariu, Radu 13 Mehlitz, Patrick 13 Reich, Simeon 13 Seeger, Alberto 13 Valero, José 13 Van Ackooij, Wim 13 Ye, Jane J. 12 Bounkhel, Messaoud 12 Gasiński, Leszek 12 Goberna, Miguel Angel 12 Huynh Van Ngai 12 Pérez-Aros, Pedro 12 Thibault, Lionel 12 Yao, Liangjin 11 Borwein, Jonathan Michael 11 Cánovas, María Josefa 11 Kapustyan, Oleksiy V. 11 Théra, Michel A. 10 Anh, Nguyen Le Hoang 10 Beer, Gerald Alan 10 Chuong, Thai Doan 10 Correa, Rafael 10 Dang Van Hieu 10 Hamel, Andreas H. 10 Henrion, René 10 Outrata, Jiří V. 10 Parra, Juan 10 Phan, Hung M. 10 Volle, Michel 10 Wachsmuth, Gerd 10 Zhang, Jie 9 Castaing, Charles 9 Gorban, Nataliia V. 9 Luke, D. Russell 9 Marigonda, Antonio 9 Martínez-Legaz, Juan-Enrique 9 Movahedian, Nooshin 9 Nobakhtian, Soghra 9 Penot, Jean-Paul 9 Phan Quôc Khánh 9 Royset, Johannes O. 9 Thao, Nguyen Hieu 9 Vũ, Bằng Công 9 Zeng, Shengda 8 Apkarian, Pierre 8 Attouch, Hedy 8 Chen, Yanhong 8 Colombo, Giovanni 8 da Cruz Neto, João Xavier 8 Dao, Minh Ngoc 8 Hu, Yijun 8 Huang, Nan-Jing 8 Karamzin, Dmitry Yu. 8 Le, Ba Khiet 8 Nam, Nguyen Mau 8 Pini, Rita 8 Rudloff, Birgit 8 Sun, Xiangkai 8 Tam, Matthew K. 8 Winkert, Patrick 8 Zhang, Binbin 8 Zhukovskiĭ, Sergeĭ Evgen’evich 7 Aragón Artacho, Francisco Javier 7 Azzam-Laouir, Dalila 7 Bello Cruz, Jose Yunier 7 Bianchi, Monica 7 Cibulka, Radek 7 de Oliveira, Welington Luis 7 Holá, Ľubica 7 Izmailov, Alekseĭ F. 7 Kalita, Piotr 7 Li, Shengjie 7 Lindstrom, Scott B. 7 Motta, Monica 7 Moursi, Walaa M. 7 Oliveira, Paulo Roberto 7 Shahzad, Naseer 7 Tang, Yuchao 7 Torki, Mounir 6 Ansari, Qamrul Hasan ...and 1,704 more Authors
all top 5

#### Cited in 266 Journals

 153 Journal of Optimization Theory and Applications 145 Set-Valued and Variational Analysis 102 Optimization 80 SIAM Journal on Optimization 65 Journal of Mathematical Analysis and Applications 60 Mathematical Programming. Series A. Series B 55 Optimization Letters 47 Journal of Global Optimization 39 Computational Optimization and Applications 37 Positivity 34 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 34 SIAM Journal on Control and Optimization 30 Vietnam Journal of Mathematics 22 Journal of Fixed Point Theory and Applications 21 Numerical Functional Analysis and Optimization 21 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 19 Journal of Differential Equations 16 Applicable Analysis 16 Journal of Convex Analysis 15 Discrete and Continuous Dynamical Systems. Series B 15 Fixed Point Theory and Applications 14 Applied Mathematics and Optimization 14 Optimization Methods & Software 13 Annals of Operations Research 11 Journal of Mathematical Imaging and Vision 11 Mathematical Problems in Engineering 11 Journal of Inequalities and Applications 11 SIAM Journal on Imaging Sciences 10 Applied Mathematics and Computation 10 Results in Mathematics 10 Calculus of Variations and Partial Differential Equations 10 Mediterranean Journal of Mathematics 10 Journal of Industrial and Management Optimization 9 Topology and its Applications 9 Operations Research Letters 9 Numerical Algorithms 9 Discrete and Continuous Dynamical Systems 9 Abstract and Applied Analysis 9 Discrete and Continuous Dynamical Systems. Series S 9 Journal of Nonlinear and Variational Analysis 8 Mathematics of Operations Research 8 Journal of Mathematical Sciences (New York) 8 Journal of Function Spaces 7 Top 7 Journal of the Australian Mathematical Society 7 Journal of Nonlinear Science and Applications 6 Inverse Problems 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 Proceedings of the American Mathematical Society 6 Journal of Scientific Computing 6 European Journal of Operational Research 6 Computational and Applied Mathematics 6 Mathematical Methods of Operations Research 6 Boundary Value Problems 6 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 5 Journal of Mathematical Economics 5 Linear Algebra and its Applications 5 Advances in Computational Mathematics 5 Communications in Contemporary Mathematics 5 Nonlinear Analysis. Real World Applications 5 Mathematical Control and Related Fields 4 Mathematical Methods in the Applied Sciences 4 Beiträge zur Algebra und Geometrie 4 Journal of Functional Analysis 4 Rendiconti del Circolo Matemàtico di Palermo. Serie II 4 Transactions of the American Mathematical Society 4 Asia-Pacific Journal of Operational Research 4 SIAM Journal on Mathematical Analysis 4 SIAM Journal on Scientific Computing 4 Applied and Computational Harmonic Analysis 4 International Journal of Theoretical and Applied Finance 4 Journal of Dynamical and Control Systems 4 Differential Equations 4 Communications on Pure and Applied Analysis 4 Advances in Difference Equations 4 Symmetry 4 Evolution Equations and Control Theory 3 Acta Mathematica Vietnamica 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Automatica 3 Journal of Computational and Applied Mathematics 3 Systems & Control Letters 3 Acta Applicandae Mathematicae 3 Topological Methods in Nonlinear Analysis 3 Finance and Stochastics 3 Taiwanese Journal of Mathematics 3 Foundations of Computational Mathematics 3 4OR 3 Inverse Problems and Imaging 3 Numerical Algebra, Control and Optimization 3 Journal of the Operations Research Society of China 2 International Journal of Control 2 Indian Journal of Pure & Applied Mathematics 2 Israel Journal of Mathematics 2 Mathematical Notes 2 Russian Mathematical Surveys 2 Ukrainian Mathematical Journal 2 Mathematics of Computation 2 Archiv der Mathematik 2 Calcolo ...and 166 more Journals
all top 5

#### Cited in 48 Fields

 836 Operations research, mathematical programming (90-XX) 749 Calculus of variations and optimal control; optimization (49-XX) 404 Operator theory (47-XX) 288 Numerical analysis (65-XX) 167 Partial differential equations (35-XX) 154 Ordinary differential equations (34-XX) 124 General topology (54-XX) 106 Functional analysis (46-XX) 101 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 84 Real functions (26-XX) 80 Global analysis, analysis on manifolds (58-XX) 64 Systems theory; control (93-XX) 58 Dynamical systems and ergodic theory (37-XX) 52 Convex and discrete geometry (52-XX) 46 Computer science (68-XX) 43 Measure and integration (28-XX) 43 Information and communication theory, circuits (94-XX) 26 Mechanics of deformable solids (74-XX) 19 Statistics (62-XX) 17 Probability theory and stochastic processes (60-XX) 16 Approximations and expansions (41-XX) 16 Biology and other natural sciences (92-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 11 Fluid mechanics (76-XX) 10 Difference and functional equations (39-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 8 Differential geometry (53-XX) 8 Mechanics of particles and systems (70-XX) 7 Algebraic topology (55-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 General and overarching topics; collections (00-XX) 5 Mathematical logic and foundations (03-XX) 5 Nonassociative rings and algebras (17-XX) 5 Integral equations (45-XX) 4 Geometry (51-XX) 3 History and biography (01-XX) 3 Topological groups, Lie groups (22-XX) 3 Optics, electromagnetic theory (78-XX) 2 Combinatorics (05-XX) 2 Algebraic geometry (14-XX) 2 Category theory; homological algebra (18-XX) 2 Geophysics (86-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Manifolds and cell complexes (57-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX)