Characterizations of Approximate Duality and Saddle Point Theorems for Nonsmooth Robust Vector Optimization

DOI10.1080/01630563.2019.1660891zbMath1434.90114OpenAlexW2971419418WikidataQ127299881 ScholiaQ127299881MaRDI QIDQ5213382

Xiang-Kai Sun, Li-Ping Tang, Jing Zeng

Publication date: 3 February 2020

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630563.2019.1660891

zbMATH Keywords

approximate quasi solutionsquasi saddle pointsrobust vector optimization problems

Mathematics Subject Classification ID

Minimax problems in mathematical programming (90C47) Nonconvex programming, global optimization (90C26) Multi-objective and goal programming (90C29) Optimality conditions and duality in mathematical programming (90C46) Nonsmooth analysis (49J52) Robustness in mathematical programming (90C17)

Related Items

Some characterizations of approximate solutions for robust semi-infinite optimization problems ⋮ Approximate optimality conditions and approximate duality theorems for nonlinear semi-infinite programming problems with uncertainty data ⋮ Robust approximate optimal solutions for nonlinear semi-infinite programming with uncertainty ⋮ Characterizations of robustε-quasi optimal solutions for nonsmooth optimization problems with uncertain data ⋮ Robust saddle-point criteria for multi-dimensional control optimisation problems with data uncertainty

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Approximate solutions of multiobjective optimization problems
• \(\varepsilon \)-mixed type duality for nonconvex multiobjective programs with an infinite number of constraints
• Robust duality in parametric convex optimization
• Higher-order optimality conditions for set-valued optimization
• Some properties of approximate solutions for vector optimization problem with set-valued functions
• \(\varepsilon \)-optimality and \(\varepsilon \)-Lagrangian duality for a nonconvex programming problem with an infinite number of constraints
• \(\epsilon\)-solutions in vector minimization problems
• Complete characterizations of robust strong duality for robust vector optimization problems
• Robust multiobjective optimization with application to Internet routing
• A unified characterization of multiobjective robustness via separation
• Recent advances in robust optimization: an overview
• Sequential optimality conditions for fractional optimization with applications to vector optimization
• \(\epsilon\)-duality of nondifferentiable nonconvex multiobjective programming
• Dual approaches to characterize robust optimal solution sets for a class of uncertain optimization problems
• Farkas-type results for vector-valued functions with applications
• Existence and optimality conditions for approximate solutions to vector optimization problems
• \(\epsilon\)-optimality conditions of vector optimization problems with set-valued maps based on the algebraic interior in real linear spaces
• Vector optimization. Set-valued and variational analysis.
• Necessary optimality conditions and saddle points for approximate optimization in Banach space
• Nonsmooth multiobjective programming and constraint qualifications
• Strong Duality in Robust Convex Programming: Complete Characterizations
• Theory and Applications of Robust Optimization
• Duality in Vector Optimization
• Optimization and nonsmooth analysis
• Semismooth and Semiconvex Functions in Constrained Optimization
• Optimality and duality for robust multiobjective optimization problems

This page was built for publication: Characterizations of Approximate Duality and Saddle Point Theorems for Nonsmooth Robust Vector Optimization