DeepONet Based Preconditioning Strategies for Solving Parametric Linear Systems of Equations: DeepONet based preconditioning strategies for solving parametric linear systems of equations

Authors: Alena Kopaničáková, George Em Karniadakis

Source: SIAM Journal on Scientific Computing. 47:C151-C181

Subject Terms: Large-scale problems in mathematical programming, Iterative numerical methods for linear systems, operator learning, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, preconditioning, Learning and adaptive systems in artificial intelligence, FOS: Mathematics, Krylov methods, Preconditioners for iterative methods, spectral bias, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), hybridization

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Access URL: http://arxiv.org/abs/2401.02016

Two sufficient descent spectral conjugate gradient algorithms for unconstrained optimization with application

Authors: Ibrahim, Sulaiman Mohammed, Salihu, Nasiru

Source: Optimization and Engineering. 26:655-679

Subject Terms: Large-scale problems in mathematical programming, Applications of mathematical programming, Numerical mathematical programming methods, Nonlinear programming, conjugate gradient, Minimax problems in mathematical programming, spectral parameter, image restoration, large scale optimization, convergence analysis

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Access URL: https://zbmath.org/8008782
https://doi.org/10.1007/s11081-024-09899-z

The MDM Algorithm and the Sylvester Problem: The MDM algorithm and the Sylvester problem

Authors: Malozemov, V. N., Solov'eva, N. A., Tamasyan, G. Sh.

Source: Computational Mathematics and Mathematical Physics. 64:1396-1412

Subject Terms: quadratic programming, Quadratic programming, Sylvester problem, MDM algorithm, Minimax problems in mathematical programming, \(n\)-dimensional polytopes

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Sampling and Update Frequencies in Proximal Variance-Reduced Stochastic Gradient Methods: Sampling and update frequencies in proximal variance-reduced stochastic gradient methods

Authors: Martin Morin, Pontus Giselsson

Source: Journal of Optimization Theory and Applications. 205

Subject Terms: Large-scale problems in mathematical programming, FOS: Computer and information sciences, Convex programming, sampling, Computer Science - Machine Learning, 0211 other engineering and technologies, SAGA, L-SVRG, 02 engineering and technology, stochastic gradient, Machine Learning (cs.LG), Numerical mathematical programming methods, epoch length, Nonlinear programming, Optimization and Control (math.OC), variance-reduced, 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Primary 65K05, Secondary 90C06, 90C25, 90C30, 68Q25, Mathematics - Optimization and Control

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Access URL: http://arxiv.org/abs/2002.05545

Robust vertex centdian facility location problem on tree networks

Authors: Soudabeh Seyyedi Ghomi, Fahimeh Baroughi

Source: Annals of Operations Research. 341:1135-1149

Subject Terms: Discrete location and assignment, centdian location problem, minmax criterion, Deterministic network models in operations research, robust optimization, minmax regret, Minimax problems in mathematical programming

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First-Order Penalty Methods for Bilevel Optimization: First-order penalty methods for bilevel optimization

Authors: Zhaosong Lu, Sanyou Mei

Source: SIAM Journal on Optimization. 34:1937-1969

Subject Terms: bilevel optimization, first-order methods, FOS: Computer and information sciences, Computer Science - Machine Learning, 0211 other engineering and technologies, operation complexity, Machine Learning (stat.ML), 02 engineering and technology, Numerical Analysis (math.NA), Nonconvex programming, global optimization, Minimax problems in mathematical programming, Machine Learning (cs.LG), penalty methods, Numerical mathematical programming methods, Nonlinear programming, Statistics - Machine Learning, Optimization and Control (math.OC), FOS: Mathematics, minimax optimization, Mathematics - Numerical Analysis, 90C26, 90C30, 90C47, 90C99, 65K05, Mathematics - Optimization and Control

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Access URL: http://arxiv.org/abs/2301.01716

Optimality conditions and sensitivity analysis in parametric nonconvex minimax programming

Authors: D. T. V. An, N. H. Hung, D. T. Ngoan, N. V. Tuyen

Source: Journal of Global Optimization. 90:53-72

Subject Terms: optimality conditions, Mordukhovich subdifferentials, Sensitivity, stability, parametric optimization, metric qualification condition, optimal value function, Optimality conditions and duality in mathematical programming, Minimax problems in mathematical programming, subdifferentiation of maximum functions, Multi-objective and goal programming, parametric nonconvex minimax programming

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Access URL: https://zbmath.org/7914897
https://doi.org/10.1007/s10898-024-01388-y

Nonlinear distributionally robust optimization

Authors: Sheriff, Mohammed Rayyan, Mohajerin Esfahani, Peyman^{Aff1, IDs10107024021517_cor1}

Source: Mathematical Programming: A Publication of the Mathematical Optimization Society. :1-60

Global algorithm for effectively solving min-max affine fractional programs

Authors: Jiao, Hongwei, Sun, Yudong, Wang, Wenjie, Shang, Youlin

Source: Journal of Applied Mathematics and Computing. 70:1787-1811

Subject Terms: algorithmic complexity, linear relaxation technique, branch-relaxation-bound algorithm, min-max affine fractional programs, Fractional programming, Nonconvex programming, global optimization, Minimax problems in mathematical programming

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A Block Lanczos Method for Large-Scale Quadratic Minimization Problems with Orthogonality Constraints: A block Lanczos method for large-scale quadratic minimization problems with orthogonality constraints

Authors: Feng, Bo, Wu, Gang

Source: SIAM Journal on Scientific Computing. 46:A884-A905

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Large-scale problems in mathematical programming, Iterative numerical methods for linear systems, 0211 other engineering and technologies, 02 engineering and technology, Numerical Analysis (math.NA), Quadratic programming, block Krylov subspace, Nonconvex programming, global optimization, 01 natural sciences, quadratic minimization problems with orthogonality constraints, Numerical mathematical programming methods, QMPO, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, block Lanczos

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Access URL: http://arxiv.org/abs/2304.11886
https://zbmath.org/7820565
https://doi.org/10.1137/23m1568545

Designing tractable piecewise affine policies for multi-stage adjustable robust optimization

Authors: Simon Thomä, Grit Walther, Maximilian Schiffer

Source: Mathematical programming 208(1/2), 661-716 (2024). doi:10.1007/s10107-023-02053-0

Subject Terms: 0209 industrial biotechnology, adjustable optimization, 05 social sciences, 0211 other engineering and technologies, robust optimization, 02 engineering and technology, Minimax problems in mathematical programming, Approximation methods and heuristics in mathematical programming, 90C47, 90C57, 90C59, 49K35, ddc, Optimization and Control (math.OC), multi-stage problem, 0502 economics and business, Polyhedral combinatorics, branch-and-bound, branch-and-cut, FOS: Mathematics, Full Length Paper, Robust optimization, Multi-stage problem, Adjustable optimization, Approximation bounds, 90C47, 90C57, 90C59, 49K35, approximation bounds, Mathematics - Optimization and Control

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Access URL: http://arxiv.org/abs/2207.00403
https://zbmath.org/7940332
https://doi.org/10.1007/s10107-023-02053-0
https://mediatum.ub.tum.de/doc/1770766/document.pdf
https://publications.rwth-aachen.de/record/979796

Frank–Wolfe-type methods for a class of nonconvex inequality-constrained problems: Frank-Wolfe-type methods for a class of nonconvex inequality-constrained problems

Authors: Liaoyuan Zeng, Yongle Zhang, Guoyin Li, Ting Kei Pong, Xiaozhou Wang

Source: Mathematical Programming. 208:717-761

Subject Terms: Large-scale problems in mathematical programming, nonconvex constraint sets, Optimization and Control (math.OC), 0211 other engineering and technologies, FOS: Mathematics, generalized linear-optimization oracles, Frank-Wolfe variants, 02 engineering and technology, Nonconvex programming, global optimization, away-step oracles, Mathematics - Optimization and Control

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Access URL: http://arxiv.org/abs/2112.14404
https://zbmath.org/7940333
https://doi.org/10.1007/s10107-023-02055-y

Sensitivity Analysis of the Maximal Value Function with Applications in Nonconvex Minimax Programs: Sensitivity analysis of the maximal value function with applications in nonconvex minimax programs

Authors: Lei Guo, Jane J. Ye, Jin Zhang

Source: Mathematics of Operations Research. 49:536-556

Subject Terms: 0211 other engineering and technologies, 02 engineering and technology, Wolfe duality, Minimax problems in mathematical programming, 01 natural sciences, value function, sensitivity analysis, Optimization and Control (math.OC), Sensitivity, stability, parametric optimization, FOS: Mathematics, necessary optimality, nonconvex minimax problem, 90C30, 90C31, 90C47, non-Lipschitz continuity, 0101 mathematics, Mathematics - Optimization and Control

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Access URL: http://arxiv.org/abs/2303.01474
https://zbmath.org/7812933
https://doi.org/10.1287/moor.2023.1366

Min-Max Framework for Majorization-Minimization Algorithms in Signal Processing Applications: An Overview: Min-max framework for majorization-minimization algorithms in signal processing applications: an overview

Authors: Saini, Astha, Stoica, Petre, Babu, Prabhu, Arora, Aakash

Source: Foundations and Trends® in Signal Processing. 18:310-389

Subject Terms: majorization-minimization, Signal Processing (eess.SP), Applications of mathematical programming, nonconvex optimization, FOS: Electrical engineering, electronic engineering, information engineering, conjugate function, min-max problem, Electrical Engineering and Systems Science - Signal Processing, Minimax problems in mathematical programming

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Access URL: http://arxiv.org/abs/2411.07561
https://zbmath.org/7944745
https://doi.org/10.1561/2000000129

A New Inertial-Projection Method for Solving Split Generalized Mixed Equilibrium and Hierarchical Fixed Point Problems: A new inertial-projection method for solving split generalized mixed equilibrium and hierarchical fixed point problems

Authors: Oyewole, Olawale Kazeem, Mewomo, Oluwatosin Temitope

Source: Kragujevac Journal of Mathematics. 48:199-223

Subject Terms: strong convergence, pseudomonotone, hierachical fixed point, Hilbert space, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc, Existence of solutions for minimax problems, inertial, Minimax problems in mathematical programming, equilibrium problem

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Access URL: https://zbmath.org/7958438

Enhanced Balancing of Bias-Variance Tradeoff in Stochastic Estimation: A Minimax Perspective: Enhanced balancing of bias-variance tradeoff in stochastic estimation: a minimax perspective

Authors: Henry Lam, Xinyu Zhang, Xuhui Zhang

Source: Operations Research. 71:2352-2373

Subject Terms: FOS: Computer and information sciences, 0209 industrial biotechnology, finite difference, 0211 other engineering and technologies, minimax analysis, robust optimization, 02 engineering and technology, Minimax problems in mathematical programming, 01 natural sciences, stochastic estimation, Methodology (stat.ME), bias-variance tradeoff, 0101 mathematics, Statistics - Methodology

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Access URL: http://arxiv.org/abs/1902.04673
https://zbmath.org/7819194
https://doi.org/10.1287/opre.2022.2319

Interval division and linearization algorithm for minimax linear fractional program

Authors: Bo Zhang, Yuelin Gao, Xia Liu, Xiaoli Huang

Source: Numerical Algorithms. 95:839-858

Subject Terms: minimax linear fractional programming, computational complexity, Numerical mathematical programming methods, Linear programming, global optimization, decision problem, polynomial approximation algorithm, linear programming, interval partition, Fractional programming, Minimax problems in mathematical programming

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Convergence of an asynchronous block-coordinate forward-backward algorithm for convex composite optimization

Authors: Cheik Traoré, Saverio Salzo, Silvia Villa

Source: Computational Optimization and Applications

Subject Terms: Large-scale problems in mathematical programming, Decomposition methods, FOS: Computer and information sciences, Convex programming, convex optimization, forward-backward algorithm, 0211 other engineering and technologies, error bounds, 02 engineering and technology, asynchronous algorithms, stochastic quasi-Fejér sequences, Numerical mathematical programming methods, Computer Science - Distributed, Parallel, and Cluster Computing, Optimization and Control (math.OC), convergence rates, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, randomized block-coordinate descent, Distributed, Parallel, and Cluster Computing (cs.DC), parallel optimization, rate of convergence, Convex optimization, Asynchronous algorithms, Randomized block-coordinate descent, Error bounds, Stochastic quasi-Fejer sequences, Forward-backward algorithm, Convergence rates, Mathematics - Optimization and Control

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Access URL: http://arxiv.org/abs/2201.05498

Optimal algorithms for differentially private stochastic monotone variational inequalities and saddle-point problems

Authors: Digvijay Boob, Cristóbal Guzmán

Source: Mathematical Programming. 204:255-297

Subject Terms: FOS: Computer and information sciences, Convex programming, Computer Science - Machine Learning, 65K10, 49M37, 68T09, algorithmic stability, 0211 other engineering and technologies, Stochastic programming, Machine Learning (stat.ML), 02 engineering and technology, Minimax problems in mathematical programming, 01 natural sciences, Machine Learning (cs.LG), stochastic algorithms, Statistics - Machine Learning, Optimization and Control (math.OC), differential privacy, Sensitivity, stability, parametric optimization, FOS: Mathematics, saddle-point problems, 0101 mathematics, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming), Mathematics - Optimization and Control, variational inequalities

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Access URL: http://arxiv.org/abs/2104.02988
https://zbmath.org/7807810
https://doi.org/10.1007/s10107-023-01953-5

A note on the linear convergence of generalized primal-dual hybrid gradient methods

Authors: Wang, Kai, Wang, Qun

Source: Pacific Journal of Optimization. 19:551-567

Subject Terms: linear convergence rate, predictor-corrector, Variational and other types of inequalities involving nonlinear operators (general), error bound, Rate of convergence, degree of approximation, saddle point problem, Minimax problems in mathematical programming, primal-dual hybrid gradient algorithm, Numerical methods for variational inequalities and related problems

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Access URL: https://zbmath.org/7778581