Stability Properties for Parametric Linear Programs under Data Ambiguities: Stability properties for parametric linear programs under data ambiguities

Authors: Thai Doan Chuong, Cao Thanh Tinh

Source: SIAM Journal on Optimization. 35:92-115

Subject Terms: Numerical optimization and variational techniques, parametric linear program, solution map, uncertain optimization, semi-infinite programming, Optimality conditions and duality in mathematical programming, stability, Multi-objective and goal programming

File Description: application/xml; Print-Electronic

Access URL: https://zbmath.org/7966995
https://doi.org/10.1137/23m1618156
https://bura.brunel.ac.uk/handle/2438/30813

Optimality conditions for directional efficiency in set-valued optimization

Authors: Maxim, Diana-Elena

Source: Pacific Journal of Optimization. 21:1-16

Subject Terms: directional efficiency, openness, Derivatives of functions in infinite-dimensional spaces, set-valued optimization, sum stability, Optimality conditions and duality in mathematical programming, Set-valued and variational analysis, Set-valued maps in general topology

File Description: application/xml

Access URL: https://zbmath.org/8027391
https://doi.org/10.61208/pjo-2023-010

Calm Local Optimality for Nonconvex-Nonconcave Minimax Problems: Calm local optimality for nonconvex-nonconcave minimax problems

Authors: Xiaoxiao Ma, Wei Yao, Jane J. Ye, Jin Zhang

Source: Set-Valued and Variational Analysis. 33

Subject Terms: first-order optimality condition, second-order optimality condition, Nonsmooth analysis, Nonconvex programming, global optimization, Nonlinear programming, local optimality, Optimization and Control (math.OC), Sensitivity, stability, parametric optimization, FOS: Mathematics, Hierarchical games (including Stackelberg games), Optimality conditions and duality in mathematical programming, minimax problem, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming), Mathematics - Optimization and Control, calmness

File Description: application/xml

Access URL: http://arxiv.org/abs/2306.17443
https://zbmath.org/8035740
https://doi.org/10.1007/s11228-025-00750-w

Metrically Levitin–Polyak well-posed parametric set optimization problem: Metrically Levitin-Polyak well-posed parametric set optimization problem

Authors: Biswajit Tahu, Mansi Dhingra, Pankaj Kumar Garg

Source: OPSEARCH. 62:249-267

Subject Terms: excess functions, parametric set optimization problem, Hausdorff distance, Sensitivity, stability, parametric optimization, Levitin-Polyak well-posedness, \( \alpha \)-weak minimal solution, Optimality conditions and duality in mathematical programming, Nonconvex programming, global optimization, Operations research and management science, Set-valued and variational analysis

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Extended convergence analysis of the Scholtes-type regularization for cardinality-constrained optimization problems

Authors: Sebastian Lämmel, Vladimir Shikhman

Source: Mathematical Programming. 211:207-243

Subject Terms: index, nondegenerate T-stationarity, 0211 other engineering and technologies, Scholtes-type regularization method, 02 engineering and technology, cardinality-constrained optimization problem, Nonconvex programming, global optimization, 01 natural sciences, Optimization and Control (math.OC), FOS: Mathematics, 90C26, 49M20, Optimality conditions and duality in mathematical programming, 0101 mathematics, genericity, Mathematics - Optimization and Control

File Description: application/xml

Access URL: http://arxiv.org/abs/2212.14577
https://zbmath.org/8035685
https://doi.org/10.1007/s10107-024-02082-3

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

File Description: application/xml

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

Epsilon-subdifferentiability for interval-valued functions and its application in interval optimization problems

Authors: Krishan Kumar, Debdas Ghosh, Jiawei Chen, Jen-Chih Yao

Source: Computational and Applied Mathematics. 44

Subject Terms: interval optimization, Nonlinear programming, interval minimax optimization, Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems, \(gH_\epsilon\)-subdifferential, Optimality conditions and duality in mathematical programming, \(\epsilon\)-optimal solution

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Access URL: https://zbmath.org/8034196
https://doi.org/10.1007/s40314-025-03151-9

Duality-Based Single-Level Reformulations of Bilevel Optimization Problems: Duality-based single-level reformulations of bilevel optimization problems

Authors: Stephan Dempe, Patrick Mehlitz

Source: Journal of Optimization Theory and Applications. 205

Subject Terms: bilevel optimization, Nonlinear programming, Lagrange duality, Optimization and Control (math.OC), Mond-Weir duality, FOS: Mathematics, Optimality conditions and duality in mathematical programming, Wolfe duality, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming), Mathematics - Optimization and Control, 90C30, 90C33, 90C46, implicit variables

File Description: application/xml

Access URL: http://arxiv.org/abs/2405.07672

A new dual-based cutting plane algorithm for nonlinear adjustable robust optimization

Authors: Abbas Khademi, Ahmadreza Marandi, Majid Soleimani-damaneh

Source: Journal of Global Optimization. 89:559-595

Subject Terms: 90C17, adjustable robust optimization, 0211 other engineering and technologies, 90C30, 02 engineering and technology, biconvex programming, 90C46, Robustness in mathematical programming, Nonconvex programming, global optimization, 01 natural sciences, perspective function, 90C26, alternating method, Biconvex programming, Fenchel duality, Adjustable robust optimization, Perspective function, Nonlinear programming, cutting plane methods, Alternating method, Cutting plane methods, Optimality conditions and duality in mathematical programming, 0101 mathematics

File Description: application/xml

Access URL: https://zbmath.org/7878111
https://doi.org/10.1007/s10898-023-01360-2
https://research.tue.nl/en/publications/b3d959e6-b8f1-496c-be41-cbb585a49c6b
https://doi.org/10.1007/s10898-023-01360-2

Efficiency conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds

Authors: Balendu Bhooshan Upadhyay, Arnav Ghosh, Savin Treanţă

Source: Journal of Global Optimization. 89:723-744

Subject Terms: Programming in abstract spaces, theorems of alternative, multi-objective optimization, duality, semi-infinite programming, Hadamard manifolds, Optimality conditions and duality in mathematical programming, Semi-infinite programming, Multi-objective and goal programming

File Description: application/xml

Asymmetry in the complexity of the multi-commodity network pricing problem

Authors: Quang Minh Bui, Margarida Carvalho, José Neto

Source: Mathematical Programming. 208:425-461

Subject Terms: Convex programming, conjugate model, G.1.6, 0211 other engineering and technologies, complexity asymmetry, Microeconomic theory (price theory and economic markets), G.2.2, 02 engineering and technology, Programming involving graphs or networks, network pricing problem, Optimization and Control (math.OC), strong bilevel feasibility, FOS: Mathematics, 90C46, 90C25, 90C35, Hierarchical games (including Stackelberg games), Optimality conditions and duality in mathematical programming, Mathematics - Optimization and Control

File Description: application/xml

Access URL: http://arxiv.org/abs/2212.10673
https://zbmath.org/7940326
https://doi.org/10.1007/s10107-023-02043-2

A PRP Type Conjugate Gradient Method Without Truncation for Nonconvex Vector Optimization: A PRP type conjugate gradient method without truncation for nonconvex vector optimization

Authors: Jiawei Chen, Yushan Bai, Guolin Yu, Xiaoqing Ou, Xiaolong Qin

Source: Journal of Optimization Theory and Applications. 204

Subject Terms: global convergence, vector optimization, Pareto critical point, Nonlinear programming, conjugate gradient method, robust function, Optimality conditions and duality in mathematical programming, Multi-objective and goal programming

File Description: application/xml

Approximate weak efficiency of the set-valued optimization problem with variable ordering structures

Authors: Zhiang Zhou, Wenbin Wei, Fei Huang, Kequan Zhao

Source: Journal of Combinatorial Optimization. 48

Subject Terms: scalarization, set-valued maps, approximate weakly efficient solution, variable ordering structures, Optimality conditions and duality in mathematical programming, Nonconvex programming, global optimization, Multi-objective and goal programming, Convexity of real functions of several variables, generalizations, Set-valued and variational analysis

File Description: application/xml

Constraint Qualifications and Optimality Criteria for Nonsmooth Multiobjective Programming Problems on Hadamard Manifolds: Constraint qualifications and optimality criteria for nonsmooth multiobjective programming problems on Hadamard manifolds

Authors: Balendu Bhooshan Upadhyay, Arnav Ghosh, Savin Treanţă

Source: Journal of Optimization Theory and Applications. 200:794-819

Subject Terms: Programming in abstract spaces, optimality conditions, constraint qualifications, Nonlinear programming, Hadamard manifolds, Optimality conditions and duality in mathematical programming, Multi-objective and goal programming, mathematical programming

File Description: application/xml

Access URL: https://zbmath.org/7802208
https://doi.org/10.1007/s10957-023-02301-5

Higher order strict global minimizers in non-differentiable multiobjective optimization involving higher order invexity and variational inequality

Authors: Sahay, Rishi Rajan, Bhatia, Guneet

Source: OPSEARCH. 61:226-244

Subject Terms: optimality, variational-like inequality problem, Nonsmooth analysis, duality, multiobjective optimization, higher order strong invexity, Optimality conditions and duality in mathematical programming, higher order strict minimizer, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming), Multi-objective and goal programming

File Description: application/xml

Access URL: https://zbmath.org/7814732
https://doi.org/10.1007/s12597-023-00670-z

Constraint Qualifications for Nonsmooth Multiobjective Programming Problems with Switching Constraints on Hadamard Manifolds: Constraint qualifications for nonsmooth multiobjective programming problems with switching constraints on Hadamard manifolds

Authors: Balendu Bhooshan Upadhyay, Arnav Ghosh, Nader Kanzi, Hamed Soroush

Source: Bulletin of the Malaysian Mathematical Sciences Society. 47

Subject Terms: Programming in abstract spaces, switching constraints, optimality conditions, multi-objective optimization, constraint qualifications, Pareto efficiency, Hadamard manifolds, Optimality conditions and duality in mathematical programming, Semi-infinite programming, Multi-objective and goal programming

File Description: application/xml

Access URL: https://zbmath.org/7850944
https://doi.org/10.1007/s40840-024-01701-8

Approximate Benson properly efficient solutions for set-valued equilibrium problems

Authors: Zhou, Zhiang, Huang, Fei, Ansari, Qamrul Hasan

Source: Positivity. 28

Subject Terms: scalarization, set-valued equilibrium problem, nonemptiness, Optimality conditions and duality in mathematical programming, approximate Benson properly efficient solution, Nonconvex programming, global optimization, Multi-objective and goal programming, connectedness, Convexity of real functions of several variables, generalizations

File Description: application/xml

Constraint qualifications and optimality conditions for nonsmooth multiobjective mathematical programming problems with vanishing constraints on Hadamard manifolds via convexificators

Authors: B.B. Upadhyay, Arnav Ghosh, Nader Kanzi

Source: Journal of Mathematical Analysis and Applications. 542:128873

Subject Terms: Programming in abstract spaces, constraint qualifications, convexificators, Hadamard manifolds, Optimality conditions and duality in mathematical programming, vanishing constraints, Multi-objective and goal programming

File Description: application/xml

Access URL: https://zbmath.org/7941017
https://doi.org/10.1016/j.jmaa.2024.128873

Optimality Conditions and Duality for MultiobjectiveSemi-infinite Optimization Problems with SwitchingConstraints on Hadamard Manifolds: Optimality conditions and duality for multiobjective semi-infinite optimization problems with switching constraints on Hadamard manifolds

Authors: Upadhyay, Balendu Bhooshan, Ghosh, Arnav

Source: Positivity. 28

Subject Terms: Programming in abstract spaces, switching constraints, constraint qualifications, Pareto efficiency, duality, multiobjective optimization, semi-infinite programming, Hadamard manifolds, Optimality conditions and duality in mathematical programming, Semi-infinite programming, Multi-objective and goal programming

File Description: application/xml

Second-Order Optimality Conditions and Duality for Multiobjective Semi-Infinite Programming Problems on Hadamard Manifolds: Second-order optimality conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds

Authors: Upadhyay, Balendu Bhooshan, Ghosh, Arnav, Stancu-Minasian, I. M.

Source: Asia-Pacific Journal of Operational Research. 41

Subject Terms: multi-objective optimization, 0211 other engineering and technologies, duality, semi-infinite programming, second-order optimality, Hadamard manifolds, 02 engineering and technology, Optimality conditions and duality in mathematical programming, 0101 mathematics, Semi-infinite programming, 01 natural sciences, Multi-objective and goal programming

File Description: application/xml

Access URL: https://zbmath.org/7941710
https://doi.org/10.1142/s0217595923500197