Hallak, Nadav; Teboulle, Marc An adaptive Lagrangian-based scheme for nonconvex composite optimization. (English) Zbl 07811864 Math. Oper. Res. 48, No. 4, 2337-2352 (2023). MSC: 90C30 49M37 65K10 PDFBibTeX XMLCite \textit{N. Hallak} and \textit{M. Teboulle}, Math. Oper. Res. 48, No. 4, 2337--2352 (2023; Zbl 07811864) Full Text: DOI
Cohen, Eyal; Hallak, Nadav; Teboulle, Marc A dynamic alternating direction of multipliers for nonconvex minimization with nonlinear functional equality constraints. (English) Zbl 1492.90133 J. Optim. Theory Appl. 193, No. 1-3, 324-353 (2022). MSC: 90C26 90C30 65K05 90C46 PDFBibTeX XMLCite \textit{E. Cohen} et al., J. Optim. Theory Appl. 193, No. 1--3, 324--353 (2022; Zbl 1492.90133) Full Text: DOI
Sabach, Shoham; Teboulle, Marc Faster Lagrangian-based methods in convex optimization. (English) Zbl 1486.90149 SIAM J. Optim. 32, No. 1, 204-227 (2022). MSC: 90C25 65K05 PDFBibTeX XMLCite \textit{S. Sabach} and \textit{M. Teboulle}, SIAM J. Optim. 32, No. 1, 204--227 (2022; Zbl 1486.90149) Full Text: DOI arXiv
Hallak, Nadav; Teboulle, Marc Finding second-order stationary points in constrained minimization: a feasible direction approach. (English) Zbl 1450.90034 J. Optim. Theory Appl. 186, No. 2, 480-503 (2020). MSC: 90C26 90C30 65K05 90C46 90C31 PDFBibTeX XMLCite \textit{N. Hallak} and \textit{M. Teboulle}, J. Optim. Theory Appl. 186, No. 2, 480--503 (2020; Zbl 1450.90034) Full Text: DOI
Teboulle, Marc; Vaisbourd, Yakov Novel proximal gradient methods for nonnegative matrix factorization with sparsity constraints. (English) Zbl 1442.90154 SIAM J. Imaging Sci. 13, No. 1, 381-421 (2020). MSC: 90C26 90C30 49M37 65K10 PDFBibTeX XMLCite \textit{M. Teboulle} and \textit{Y. Vaisbourd}, SIAM J. Imaging Sci. 13, No. 1, 381--421 (2020; Zbl 1442.90154) Full Text: DOI
Luke, D. Russell; Teboulle, Marc; Thao, Nguyen H. Necessary conditions for linear convergence of iterated expansive, set-valued mappings. (English) Zbl 1439.49032 Math. Program. 180, No. 1-2 (A), 1-31 (2020). MSC: 49J53 65K10 49K40 49M05 49M27 65K05 90C26 PDFBibTeX XMLCite \textit{D. R. Luke} et al., Math. Program. 180, No. 1--2 (A), 1--31 (2020; Zbl 1439.49032) Full Text: DOI arXiv
Luke, D. Russell; Sabach, Shoham; Teboulle, Marc Optimization on spheres: models and proximal algorithms with computational performance comparisons. (English) Zbl 1499.90175 SIAM J. Math. Data Sci. 1, No. 3, 408-445 (2019). MSC: 90C26 49M99 65K10 PDFBibTeX XMLCite \textit{D. R. Luke} et al., SIAM J. Math. Data Sci. 1, No. 3, 408--445 (2019; Zbl 1499.90175) Full Text: DOI arXiv
Sabach, Shoham; Teboulle, Marc Lagrangian methods for composite optimization. (English) Zbl 1446.90126 Kimmel, Ron (ed.) et al., Processing, analyzing and learning of images, shapes, and forms. Part 2. Amsterdam: Elsevier/North Holland. Handb. Numer. Anal. 20, 401-436 (2019). MSC: 90C25 65K05 90C06 90C26 PDFBibTeX XMLCite \textit{S. Sabach} and \textit{M. Teboulle}, Handb. Numer. Anal. 20, 401--436 (2019; Zbl 1446.90126) Full Text: DOI
Bauschke, Heinz H.; Bolte, Jérôme; Chen, Jiawei; Teboulle, Marc; Wang, Xianfu On linear convergence of non-Euclidean gradient methods without strong convexity and Lipschitz gradient continuity. (English) Zbl 1429.65121 J. Optim. Theory Appl. 182, No. 3, 1068-1087 (2019). MSC: 65K05 90C26 90C30 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., J. Optim. Theory Appl. 182, No. 3, 1068--1087 (2019; Zbl 1429.65121) Full Text: DOI
Sabach, Shoham; Teboulle, Marc; Voldman, Sergey A smoothing alternating minimization-based algorithm for clustering with sum-min of duclidean norms. (English) Zbl 1474.90360 Pure Appl. Funct. Anal. 3, No. 4, 653-679 (2018). MSC: 90C26 90C30 49N45 65K05 PDFBibTeX XMLCite \textit{S. Sabach} et al., Pure Appl. Funct. Anal. 3, No. 4, 653--679 (2018; Zbl 1474.90360) Full Text: Link
Bolte, Jérôme; Sabach, Shoham; Teboulle, Marc Nonconvex Lagrangian-based optimization: monitoring schemes and global convergence. (English) Zbl 1440.90072 Math. Oper. Res. 43, No. 4, 1210-1232 (2018). MSC: 90C30 49M37 65K10 PDFBibTeX XMLCite \textit{J. Bolte} et al., Math. Oper. Res. 43, No. 4, 1210--1232 (2018; Zbl 1440.90072) Full Text: DOI arXiv Link
Bolte, Jérôme; Sabach, Shoham; Teboulle, Marc; Vaisbourd, Yakov First order methods beyond convexity and Lipschitz gradient continuity with applications to quadratic inverse problems. (English) Zbl 1402.90118 SIAM J. Optim. 28, No. 3, 2131-2151 (2018). MSC: 90C25 26B25 49M27 52A41 65K05 PDFBibTeX XMLCite \textit{J. Bolte} et al., SIAM J. Optim. 28, No. 3, 2131--2151 (2018; Zbl 1402.90118) Full Text: DOI arXiv
Teboulle, Marc A simplified view of first order methods for optimization. (English) Zbl 1391.90482 Math. Program. 170, No. 1 (B), 67-96 (2018). MSC: 90C25 65K05 PDFBibTeX XMLCite \textit{M. Teboulle}, Math. Program. 170, No. 1 (B), 67--96 (2018; Zbl 1391.90482) Full Text: DOI
Luke, D. Russell; Sabach, Shoham; Teboulle, Marc; Zatlawey, Kobi A simple globally convergent algorithm for the nonsmooth nonconvex single source localization problem. (English) Zbl 1386.90117 J. Glob. Optim. 69, No. 4, 889-909 (2017). MSC: 90C26 90C90 49M37 65K05 PDFBibTeX XMLCite \textit{D. R. Luke} et al., J. Glob. Optim. 69, No. 4, 889--909 (2017; Zbl 1386.90117) Full Text: DOI
Bauschke, Heinz H.; Bolte, Jérôme; Teboulle, Marc A descent lemma beyond Lipschitz gradient continuity: first-order methods revisited and applications. (English) Zbl 1364.90251 Math. Oper. Res. 42, No. 2, 330-348 (2017). MSC: 90C25 65K05 PDFBibTeX XMLCite \textit{H. H. Bauschke} et al., Math. Oper. Res. 42, No. 2, 330--348 (2017; Zbl 1364.90251) Full Text: DOI Link
Beck, Amir; Sabach, Shoham; Teboulle, Marc An alternating semiproximal method for nonconvex regularized structured total least squares problems. (English) Zbl 1346.90676 SIAM J. Matrix Anal. Appl. 37, No. 3, 1129-1150 (2016). MSC: 90C26 90C30 49N45 65K05 PDFBibTeX XMLCite \textit{A. Beck} et al., SIAM J. Matrix Anal. Appl. 37, No. 3, 1129--1150 (2016; Zbl 1346.90676) Full Text: DOI
Shefi, Ron; Teboulle, Marc On the rate of convergence of the proximal alternating linearized minimization algorithm for convex problems. (English) Zbl 1338.90306 EURO J. Comput. Optim. 4, No. 1, 27-46 (2016). MSC: 90C25 49M27 65K05 PDFBibTeX XMLCite \textit{R. Shefi} and \textit{M. Teboulle}, EURO J. Comput. Optim. 4, No. 1, 27--46 (2016; Zbl 1338.90306) Full Text: DOI
Beck, Amir; Teboulle, Marc A fast dual proximal gradient algorithm for convex minimization and applications. (English) Zbl 1408.90232 Oper. Res. Lett. 42, No. 1, 1-6 (2014). MSC: 90C25 65K05 PDFBibTeX XMLCite \textit{A. Beck} and \textit{M. Teboulle}, Oper. Res. Lett. 42, No. 1, 1--6 (2014; Zbl 1408.90232) Full Text: DOI
Bolte, Jérôme; Sabach, Shoham; Teboulle, Marc Proximal alternating linearized minimization for nonconvex and nonsmooth problems. (English) Zbl 1297.90125 Math. Program. 146, No. 1-2 (A), 459-494 (2014). MSC: 90C26 90C30 49M37 65K10 47J25 49M27 PDFBibTeX XMLCite \textit{J. Bolte} et al., Math. Program. 146, No. 1--2 (A), 459--494 (2014; Zbl 1297.90125) Full Text: DOI
Shefi, Ron; Teboulle, Marc Rate of convergence analysis of decomposition methods based on the proximal method of multipliers for convex minimization. (English) Zbl 1291.90176 SIAM J. Optim. 24, No. 1, 269-297 (2014). MSC: 90C25 65K10 49M29 PDFBibTeX XMLCite \textit{R. Shefi} and \textit{M. Teboulle}, SIAM J. Optim. 24, No. 1, 269--297 (2014; Zbl 1291.90176) Full Text: DOI
Luss, Ronny; Teboulle, Marc Conditional gradient algorithms for rank-one matrix approximations with a sparsity constraint. (English) Zbl 1263.90094 SIAM Rev. 55, No. 1, 65-98 (2013). MSC: 90C30 62H25 49M37 65K05 PDFBibTeX XMLCite \textit{R. Luss} and \textit{M. Teboulle}, SIAM Rev. 55, No. 1, 65--98 (2013; Zbl 1263.90094) Full Text: DOI arXiv
Auslender, Alfred; Shefi, Ron; Teboulle, Marc A moving balls approximation method for a class of smooth constrained minimization problems. (English) Zbl 1229.90085 SIAM J. Optim. 20, No. 6, 3232-3259 (2010). Reviewer: Rembert Reemtsen (Cottbus) MSC: 90C06 90C25 90C20 65K05 65K15 PDFBibTeX XMLCite \textit{A. Auslender} et al., SIAM J. Optim. 20, No. 6, 3232--3259 (2010; Zbl 1229.90085) Full Text: DOI
Beck, Amir; Teboulle, Marc A fast iterative shrinkage-thresholding algorithm for linear inverse problems. (English) Zbl 1175.94009 SIAM J. Imaging Sci. 2, No. 1, 183-202 (2009). MSC: 94A08 68U10 65F22 PDFBibTeX XMLCite \textit{A. Beck} and \textit{M. Teboulle}, SIAM J. Imaging Sci. 2, No. 1, 183--202 (2009; Zbl 1175.94009) Full Text: DOI Link
Auslender, Alfred; Teboulle, Marc Projected subgradient methods with non-Euclidean distances for non-differentiable convex minimization and variational inequalities. (English) Zbl 1190.90118 Math. Program. 120, No. 1 (B), 27-48 (2009). MSC: 90C25 90C33 65K05 PDFBibTeX XMLCite \textit{A. Auslender} and \textit{M. Teboulle}, Math. Program. 120, No. 1 (B), 27--48 (2009; Zbl 1190.90118) Full Text: DOI
Beck, Amir; Ben-Tal, Aharon; Teboulle, Marc Finding a global optimal solution for a quadratically constrained fractional quadratic problem with applications to the regularized total least squares. (English) Zbl 1115.65065 SIAM J. Matrix Anal. Appl. 28, No. 2, 425-445 (2006). Reviewer: Efstratios Rappos (Athens) MSC: 65K05 90C20 90C32 90C26 PDFBibTeX XMLCite \textit{A. Beck} et al., SIAM J. Matrix Anal. Appl. 28, No. 2, 425--445 (2006; Zbl 1115.65065) Full Text: DOI Link
Beck, Amir; Teboulle, Marc A conditional gradient method with linear rate of convergence for solving convex linear systems. (English) Zbl 1138.90440 Math. Methods Oper. Res. 59, No. 2, 235-247 (2004). MSC: 90C25 90C60 65K05 90C05 90C20 PDFBibTeX XMLCite \textit{A. Beck} and \textit{M. Teboulle}, Math. Methods Oper. Res. 59, No. 2, 235--247 (2004; Zbl 1138.90440) Full Text: DOI
Auslender, Alfred; Teboulle, Marc Lagrangian duality and related multiplier methods for variational inequality problems. (English) Zbl 0996.49005 SIAM J. Optim. 10, No. 4, 1097-1115 (2000). MSC: 49J40 90C33 49N15 65K10 PDFBibTeX XMLCite \textit{A. Auslender} and \textit{M. Teboulle}, SIAM J. Optim. 10, No. 4, 1097--1115 (2000; Zbl 0996.49005) Full Text: DOI
Auslender, Alfred; Teboulle, Marc; Ben-Tiba, Sami Coupling the logarithmic-quadratic proximal method and the block nonlinear Gauss-Seidel algorithm for linearly constrained convex minimization. (English) Zbl 0944.65066 Théra, Michel (ed.) et al., Ill-posed variational problems and regularization techniques. Proceedings of a workshop, Univ. of Trier, Germany, September 3-5, 1998. Berlin: Springer. Lect. Notes Econ. Math. Syst. 477, 35-47 (1999). MSC: 65K05 90C25 PDFBibTeX XMLCite \textit{A. Auslender} et al., Lect. Notes Econ. Math. Syst. 477, 35--47 (1999; Zbl 0944.65066)
Auslender, Alfred; Teboulle, Marc; Ben-Tiba, Sami A logarithmic-quadratic proximal method for variational inequalities. (English) Zbl 1039.90529 Comput. Optim. Appl. 12, No. 1-3, 31-40 (1999). MSC: 90C33 49J40 65K05 90C51 PDFBibTeX XMLCite \textit{A. Auslender} et al., Comput. Optim. Appl. 12, No. 1--3, 31--40 (1999; Zbl 1039.90529) Full Text: DOI
Iusem, Alfredo N.; Svaiter, B. F.; Teboulle, Marc Multiplicative interior gradient methods for minimization over the nonnegative orthant. (English) Zbl 0841.49012 SIAM J. Control Optimization 34, No. 1, 389-406 (1996). MSC: 90C52 90C25 90C30 65K10 PDFBibTeX XMLCite \textit{A. N. Iusem} et al., SIAM J. Control Optim. 34, No. 1, 389--406 (1996; Zbl 0841.49012) Full Text: DOI
Chen, Gong; Teboulle, Marc A proximal-based deomposition method for compositions method for convex minimization problems. (English) Zbl 0823.90097 Math. Program. 64, No. 1 (A), 81-101 (1994). Reviewer: S.Mititelu (Bucureşti) MSC: 90C25 90C60 65Y05 PDFBibTeX XMLCite \textit{G. Chen} and \textit{M. Teboulle}, Math. Program. 64, No. 1 (A), 81--101 (1994; Zbl 0823.90097) Full Text: DOI
Iusem, Alfredo N.; Teboulle, Marc A regularized dual-based iterative method for a class of image reconstruction problems. (English) Zbl 0793.65046 Inverse Probl. 9, No. 6, 679-696 (1993). Reviewer: N.A.Warsi (Stone Mountain) MSC: 65K05 90C06 94A12 90C20 PDFBibTeX XMLCite \textit{A. N. Iusem} and \textit{M. Teboulle}, Inverse Probl. 9, No. 6, 679--696 (1993; Zbl 0793.65046) Full Text: DOI
Ben-Tal, Aharon; Teboulle, Marc; Yang, Wei H. A least-squares-based method for a class of nonsmooth minimization problems with applications in plasticity. (English) Zbl 0734.73097 Appl. Math. Optimization 24, No. 3, 273-288 (1991). Reviewer: V.Burjan (Praha) MSC: 74S30 74P10 74R20 65K10 49M30 74K10 74K20 PDFBibTeX XMLCite \textit{A. Ben-Tal} et al., Appl. Math. Optim. 24, No. 3, 273--288 (1991; Zbl 0734.73097) Full Text: DOI
Ben-Tal, Aharon; Teboulle, Marc A geometric property of the least squares solution of linear equations. (English) Zbl 0704.15005 Linear Algebra Appl. 139, 165-170 (1990). Reviewer: K.Burian MSC: 15A09 65F20 PDFBibTeX XMLCite \textit{A. Ben-Tal} and \textit{M. Teboulle}, Linear Algebra Appl. 139, 165--170 (1990; Zbl 0704.15005) Full Text: DOI
Ben-Tal, A.; Teboulle, M. A smoothing technique for nondifferentiable optimization problems. (English) Zbl 0683.90078 Optimization, Proc. 5th French-German Conf., Varetz/Fr 1988, Lect. Notes Math. 1405, 1-11 (1989). MSC: 90C30 65K05 PDFBibTeX XML
Ben-Tal, Aharon; Teboulle, Marc The duality between expected utility and penalty in stochastic linear programming. (English) Zbl 0577.90056 Stochastic programming, Conf. Gargnano/Italy 1983, Lect. Notes Control Inf. Sci. 76, 151-161 (1986). MSC: 90C15 65K05 PDFBibTeX XML