Toan, N. T.; Thuy, L. Q. Second-order necessary optimality conditions for an optimal control problem with nonlinear state equations. (English) Zbl 07490114 Positivity 26, No. 1, Paper No. 20, 38 p. (2022). Reviewer: Bülent Karasözen (Ankara) MSC: 49J15 49J21 49K21 90C90 93C05 PDF BibTeX XML Cite \textit{N. T. Toan} and \textit{L. Q. Thuy}, Positivity 26, No. 1, Paper No. 20, 38 p. (2022; Zbl 07490114) Full Text: DOI OpenURL
Christof, Constantin; Müller, Georg Multiobjective optimal control of a non-smooth semilinear elliptic partial differential equation. (English) Zbl 1468.35048 ESAIM, Control Optim. Calc. Var. 27, Suppl., Paper No. S13, 31 p. (2021). MSC: 35J20 49J52 49K20 58E17 90C29 PDF BibTeX XML Cite \textit{C. Christof} and \textit{G. Müller}, ESAIM, Control Optim. Calc. Var. 27, Paper No. S13, 31 p. (2021; Zbl 1468.35048) Full Text: DOI OpenURL
Gong, Yuxuan; Li, Peijun; Wang, Xu; Xu, Xiang Numerical solution of an inverse random source problem for the time fractional diffusion equation via PhaseLift. (English) Zbl 1475.35432 Inverse Probl. 37, No. 4, Article ID 045001, 23 p. (2021). Reviewer: Robert Plato (Siegen) MSC: 35R60 26A33 35A01 35A02 35R11 35R30 35R25 49M37 60G60 60H40 60J65 65M30 65M32 65T50 90C25 35K20 PDF BibTeX XML Cite \textit{Y. Gong} et al., Inverse Probl. 37, No. 4, Article ID 045001, 23 p. (2021; Zbl 1475.35432) Full Text: DOI arXiv OpenURL
de Carvalho, Pitágoras Pinheiro; Fernández-Cara, Enrique; Ferrel, Juan Bautista Límaco On the computation of Nash and Pareto equilibria for some bi-objective control problems for the wave equation. (English) Zbl 1464.35010 Adv. Comput. Math. 46, No. 5, Paper No. 73, 30 p. (2020). MSC: 35A35 35L20 35Q93 49J20 90C29 65M06 65M60 PDF BibTeX XML Cite \textit{P. P. de Carvalho} et al., Adv. Comput. Math. 46, No. 5, Paper No. 73, 30 p. (2020; Zbl 1464.35010) Full Text: DOI OpenURL
Wang, Jun; Zhao, Tingting; Xiao, Lu Existence and asymptotical behavior of the minimizer of Hartree type equation with periodic potentials. (English) Zbl 1439.35448 Complex Var. Elliptic Equ. 65, No. 5, 740-764 (2020). Reviewer: Huansong Zhou (Wuhan) MSC: 35Q55 35J61 35J20 35Q60 49J40 35B32 35A01 35B40 35R09 90C30 PDF BibTeX XML Cite \textit{J. Wang} et al., Complex Var. Elliptic Equ. 65, No. 5, 740--764 (2020; Zbl 1439.35448) Full Text: DOI OpenURL
Kravvaritis, Dimitrios C.; Yannacopoulos, Athanasios N. Variational methods in nonlinear analysis. With applications in optimization and partial differential equations. (English) Zbl 1443.49001 De Gruyter Graduate. Berlin: De Gruyter (ISBN 978-3-11-064736-5/pbk; 978-3-11-064738-9/ebook). xxv, 474 p. (2020). Reviewer: Valerii V. Obukhovskij (Voronezh) MSC: 49-02 47-02 35J20 35J25 35J50 35J57 46A55 47H04 47H05 47H09 47H10 47J20 47J25 47J30 49J35 49J40 49J50 49J52 49J53 49K20 49K35 49N15 49N60 58C30 58E05 58E30 58E35 58J05 58J32 90C25 PDF BibTeX XML Cite \textit{D. C. Kravvaritis} and \textit{A. N. Yannacopoulos}, Variational methods in nonlinear analysis. With applications in optimization and partial differential equations. Berlin: De Gruyter (2020; Zbl 1443.49001) Full Text: DOI OpenURL
Bonifacius, Lucas; Neitzel, Ira Second order optimality conditions for optimal control of quasilinear parabolic equations. (English) Zbl 1405.35095 Math. Control Relat. Fields 8, No. 1, 1-34 (2018). MSC: 35K59 49K20 90C48 PDF BibTeX XML Cite \textit{L. Bonifacius} and \textit{I. Neitzel}, Math. Control Relat. Fields 8, No. 1, 1--34 (2018; Zbl 1405.35095) Full Text: DOI OpenURL
Pu, Jiangyan; Zhang, Qi Dynamic programming principle and associated Hamilton-Jacobi-Bellman equation for stochastic recursive control problem with non-Lipschitz aggregator. (English) Zbl 1396.93135 ESAIM, Control Optim. Calc. Var. 24, No. 1, 355-376 (2018). MSC: 93E20 90C39 35K10 49L20 49L25 60H15 93C25 93C20 PDF BibTeX XML Cite \textit{J. Pu} and \textit{Q. Zhang}, ESAIM, Control Optim. Calc. Var. 24, No. 1, 355--376 (2018; Zbl 1396.93135) Full Text: DOI arXiv OpenURL
Caffarelli, L.; De Silva, D.; Savin, O. Two-phase anisotropic free boundary problems and applications to the Bellman equation in 2D. (English) Zbl 1393.35247 Arch. Ration. Mech. Anal. 228, No. 2, 477-493 (2018). Reviewer: Eugene Postnikov (Kursk) MSC: 35Q90 90C39 35R35 35B65 93E20 35B50 35J25 49L20 PDF BibTeX XML Cite \textit{L. Caffarelli} et al., Arch. Ration. Mech. Anal. 228, No. 2, 477--493 (2018; Zbl 1393.35247) Full Text: DOI arXiv OpenURL
Aronna, M. Soledad; Bonnans, J. Frédéric; Kröner, Axel Optimal control of infinite dimensional bilinear systems: application to the heat and wave equations. (English) Zbl 1454.49028 Math. Program. 168, No. 1-2 (B), 717-757 (2018); correction ibid. 170, No. 2 (A), 569-570 (2018). MSC: 49K20 35K05 35L05 90C48 PDF BibTeX XML Cite \textit{M. S. Aronna} et al., Math. Program. 168, No. 1--2 (B), 717--757 (2018; Zbl 1454.49028) Full Text: DOI arXiv OpenURL
Alla, A.; Falcone, M.; Volkwein, S. Error analysis for POD approximations of infinite horizon problems via the dynamic programming approach. (English) Zbl 1378.49025 SIAM J. Control Optim. 55, No. 5, 3091-3115 (2017). MSC: 49L20 90C39 35K20 49L25 49J20 65N99 49M25 PDF BibTeX XML Cite \textit{A. Alla} et al., SIAM J. Control Optim. 55, No. 5, 3091--3115 (2017; Zbl 1378.49025) Full Text: DOI arXiv OpenURL
Carrillo, Mauricio; Gómez, Juan Alfredo A globally convergent algorithm for a PDE-constrained optimization problem arising in electrical impedance tomography. (English) Zbl 1319.65050 Numer. Funct. Anal. Optim. 36, No. 6, 748-776 (2015). MSC: 65K10 49J20 65N21 65N30 35R30 35J25 90C53 PDF BibTeX XML Cite \textit{M. Carrillo} and \textit{J. A. Gómez}, Numer. Funct. Anal. Optim. 36, No. 6, 748--776 (2015; Zbl 1319.65050) Full Text: DOI OpenURL
Hajba, T.; Kovács, M. Solution of the convex programming problem via second order differential equation system. (English) Zbl 1265.34185 Miskolc Math. Notes 13, No. 1, 23-37 (2012). MSC: 34D05 90C25 65K05 PDF BibTeX XML Cite \textit{T. Hajba} and \textit{M. Kovács}, Miskolc Math. Notes 13, No. 1, 23--37 (2012; Zbl 1265.34185) OpenURL
Hajba, Tamás Optimizing second-order differential equation systems. (English) Zbl 1216.90066 Electron. J. Differ. Equ. 2011, Paper No. 44, 16 p. (2011). MSC: 90C25 65K05 34D05 PDF BibTeX XML Cite \textit{T. Hajba}, Electron. J. Differ. Equ. 2011, Paper No. 44, 16 p. (2011; Zbl 1216.90066) Full Text: EuDML EMIS OpenURL
Bonnans, J. Frédéric; Jaisson, Pascal Optimal control of a parabolic equation with time-dependent state constraints. (English) Zbl 1208.49024 SIAM J. Control Optim. 48, No. 7, 4550-4571 (2010). MSC: 49K20 35K05 49K40 90C25 PDF BibTeX XML Cite \textit{J. F. Bonnans} and \textit{P. Jaisson}, SIAM J. Control Optim. 48, No. 7, 4550--4571 (2010; Zbl 1208.49024) Full Text: DOI Link OpenURL
Hante, Falk M.; Leugering, Günter; Seidman, Thomas I. Modeling and analysis of modal switching in networked transport systems. (English) Zbl 1167.93005 Appl. Math. Optim. 59, No. 2, 275-292 (2009). MSC: 93A30 93C20 90B18 35K10 94C15 PDF BibTeX XML Cite \textit{F. M. Hante} et al., Appl. Math. Optim. 59, No. 2, 275--292 (2009; Zbl 1167.93005) Full Text: DOI OpenURL
Hajba, Tamás Parameter analysis of optimization methods modeled by second order differential equation. (English) Zbl 1199.65204 Alkalmazott Mat. Lapok 25, No. 2, 61-79 (2008). MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{T. Hajba}, Alkalmazott Mat. Lapok 25, No. 2, 61--79 (2008; Zbl 1199.65204) OpenURL
Griesse, Roland; Metla, Nataliya; Rösch, Arnd Convergence analysis of the SQP method for nonlinear mixed-constrained elliptic optimal control problems. (English) Zbl 1152.49023 ZAMM, Z. Angew. Math. Mech. 88, No. 10, 776-792 (2008). MSC: 49K20 35J25 90C20 PDF BibTeX XML Cite \textit{R. Griesse} et al., ZAMM, Z. Angew. Math. Mech. 88, No. 10, 776--792 (2008; Zbl 1152.49023) Full Text: DOI OpenURL
Voisei, M. D. Mathematical programming problems governed by nonlinear elliptic PDEs. (English) Zbl 1151.49021 SIAM J. Optim. 18, No. 4, 1231-1249 (2007). MSC: 49K20 35J60 90C46 49M37 35J25 PDF BibTeX XML Cite \textit{M. D. Voisei}, SIAM J. Optim. 18, No. 4, 1231--1249 (2007; Zbl 1151.49021) Full Text: DOI OpenURL
Rösch, A.; Tröltzsch, F. Sufficient second-order optimality conditions for an elliptic optimal control problem with pointwise control-state constraints. (English) Zbl 1119.49022 SIAM J. Optim. 17, No. 3, 776-794 (2006). MSC: 49K20 90C48 35J25 PDF BibTeX XML Cite \textit{A. Rösch} and \textit{F. Tröltzsch}, SIAM J. Optim. 17, No. 3, 776--794 (2006; Zbl 1119.49022) Full Text: DOI OpenURL
Ferreira, Orizon P. Convexity with respect to a differential equation. (English) Zbl 1097.34012 J. Math. Anal. Appl. 315, No. 2, 626-641 (2006). Reviewer: J. Banaś (Rzeszów) MSC: 34A99 34C99 90C99 PDF BibTeX XML Cite \textit{O. P. Ferreira}, J. Math. Anal. Appl. 315, No. 2, 626--641 (2006; Zbl 1097.34012) Full Text: DOI OpenURL
Rösch, A.; Tröltzsch, F. Sufficient second-order optimality conditions for a parabolic optimal control problem with pointwise control-state constraints. (English) Zbl 1038.49028 SIAM J. Control Optimization 42, No. 1, 138-154 (2003). MSC: 49K20 90C46 35K55 PDF BibTeX XML Cite \textit{A. Rösch} and \textit{F. Tröltzsch}, SIAM J. Control Optim. 42, No. 1, 138--154 (2003; Zbl 1038.49028) Full Text: DOI OpenURL
Arutyunov, Aram V.; Izmailov, Alexey F. Bifurcation theorems via second-order optimality conditions. (English) Zbl 1001.34031 J. Math. Anal. Appl. 262, No. 2, 564-576 (2001). Reviewer: Boris V.Loginov (Ulyanovsk) MSC: 34C23 90C49 58E07 PDF BibTeX XML Cite \textit{A. V. Arutyunov} and \textit{A. F. Izmailov}, J. Math. Anal. Appl. 262, No. 2, 564--576 (2001; Zbl 1001.34031) Full Text: DOI OpenURL
Farahi, M. H.; Rubio, J. E.; Wilson, D. A. The global control of a nonlinear wave equation. (English) Zbl 0917.49005 Int. J. Control 65, No. 1, 1-15 (1996). Reviewer: M.Brokate (Kaiserslautern) MSC: 49J20 35L70 35L05 90C05 PDF BibTeX XML Cite \textit{M. H. Farahi} et al., Int. J. Control 65, No. 1, 1--15 (1996; Zbl 0917.49005) Full Text: DOI OpenURL
Bando, M.; Hasebe, K.; Nakayama, A.; Shibata, A.; Sugiyama, Y. Structure stability of congestion in traffic dynamics. (English) Zbl 0811.90036 Japan J. Ind. Appl. Math. 11, No. 2, 203-223 (1994). MSC: 90B20 PDF BibTeX XML Cite \textit{M. Bando} et al., Japan J. Ind. Appl. Math. 11, No. 2, 203--223 (1994; Zbl 0811.90036) Full Text: DOI OpenURL
Sagan, Hans; Bishir, John W. Optimal allocation of storage space. (English) Zbl 0739.90011 Eur. J. Oper. Res. 55, No. 1, 82-90 (1991). MSC: 90B05 PDF BibTeX XML Cite \textit{H. Sagan} and \textit{J. W. Bishir}, Eur. J. Oper. Res. 55, No. 1, 82--90 (1991; Zbl 0739.90011) Full Text: DOI OpenURL
Rao, Murali; Sokołowski, Jan Differential stability of solutions to parametric optimization problems. (English) Zbl 0749.90077 Math. Methods Appl. Sci. 14, No. 4, 281-294 (1991). MSC: 90C31 PDF BibTeX XML Cite \textit{M. Rao} and \textit{J. Sokołowski}, Math. Methods Appl. Sci. 14, No. 4, 281--294 (1991; Zbl 0749.90077) Full Text: DOI OpenURL
Otero, Manuel Zwei Trajektorienverfahren zur Lösung nichtlinearer Optimierungsaufgaben. (Two trajectory methods for the solution of nonlinear optimization problems). (German) Zbl 0714.90090 Optimization 21, No. 4, 559-573 (1990). MSC: 90C30 90-08 65D15 PDF BibTeX XML Cite \textit{M. Otero}, Optimization 21, No. 4, 559--573 (1990; Zbl 0714.90090) Full Text: DOI OpenURL
Aluffi-Pentini, F.; Parisi, V.; Zirilli, F. An inexact continuous method in complementarity problems. (English) Zbl 0603.90129 Annu. Rev. Autom. Program. 13, Part 2, 19-26 (1986). MSC: 90C33 65K05 65K10 PDF BibTeX XML OpenURL
Choi, Sung-Bin; Hwang, Hark Dynamic optimization of production planning problem with periodic operation. (English) Zbl 0596.90041 Int. J. Syst. Sci. 17, 1163-1174 (1986). Reviewer: S.K.Goyal MSC: 90B30 PDF BibTeX XML Cite \textit{S.-B. Choi} and \textit{H. Hwang}, Int. J. Syst. Sci. 17, 1163--1174 (1986; Zbl 0596.90041) Full Text: DOI OpenURL
Teo, K. L.; Wilson, S. J. Convergence of a feasible directions algorithm for a distributed optimal control problem of parabolic type with terminal inequality constraints. (English) Zbl 0569.49024 J. Optimization Theory Appl. 49, 463-476 (1986). MSC: 90C99 35K20 49K20 49M20 65K10 93B40 93C05 93C20 PDF BibTeX XML Cite \textit{K. L. Teo} and \textit{S. J. Wilson}, J. Optim. Theory Appl. 49, 463--476 (1986; Zbl 0569.49024) Full Text: DOI OpenURL
Vasil’eva, V. N. On the question of optimal control over coefficients of parabolic equations. (Russian) Zbl 0587.49007 Questions of stability and optimization of dynamical systems, Collect. Artic., Irkutsk 1983, 64-74 (1983). Reviewer: U.Raitums MSC: 49J20 35K10 49J50 90C52 65D07 65K10 93B40 93C05 93C20 PDF BibTeX XML OpenURL
Teo, K. L. Convergence of a conditional gradient algorithm for relaxed controls involving first boundary value problems of parabolic type. (English) Zbl 0552.49026 Numer. Funct. Anal. Optimization 6, 457-491 (1983). Reviewer: T.Seidman MSC: 90C52 35K20 65K10 35B37 49J20 93B40 93C05 93C20 PDF BibTeX XML Cite \textit{K. L. Teo}, Numer. Funct. Anal. Optim. 6, 457--491 (1983; Zbl 0552.49026) Full Text: DOI OpenURL
Ekeland, I. Dual variational methods in non-convex optimization and differential equations. (English) Zbl 0544.49010 Mathematical theories of optimization, Proc. Conf., Genova 1981, Lect. Notes Math. 979, 108-120 (1983). Reviewer: C.L.Sandblom MSC: 49N15 49J45 90C48 49J27 49K15 49K20 49K27 58C20 58E30 37J99 35L70 PDF BibTeX XML OpenURL
Bensoussan, Alain Stochastic control by functional analysis methods. (English) Zbl 0474.93002 Studies in Mathematics and its Applications, Vol. 11. Amsterdam - New York - Oxford: North-Holland Publishing Company. XVI, 410 p. $ 58.25; Dfl. 125.00 (1982). MSC: 93-01 49J55 93E20 35J20 49J40 60H10 93E11 35J65 60G40 90C39 PDF BibTeX XML OpenURL
Sommer, Rolf Finite-Element-Approximation und semi-infinite Optimierungsaufgaben. (German) Zbl 0481.90055 Seminarber., Humboldt-Univ. Berlin, Sekt. Math. 39, 210-224 (1981). MSC: 90C05 65N06 90C34 90C90 PDF BibTeX XML Cite \textit{R. Sommer}, Seminarber., Humboldt-Univ. Berlin, Sekt. Math. 39, 210--224 (1981; Zbl 0481.90055) OpenURL
Zuckerman, Dror A diffusion process model for the optimal investment strategies of an R & D project. (English) Zbl 0439.90045 J. Appl. Probab. 17, 646-653 (1980). MSC: 90B99 PDF BibTeX XML Cite \textit{D. Zuckerman}, J. Appl. Probab. 17, 646--653 (1980; Zbl 0439.90045) Full Text: DOI OpenURL
O’Leary, Dianne P. Linear programming problems arising from partial differential equations. (English) Zbl 0407.65046 Sparse matrix computations, Proc. Symp., Knoxville 1978, 25-40 (1979). MSC: 65N22 90C05 65K05 35J25 65N99 PDF BibTeX XML OpenURL