ε-Optimality Conditions for Vector Optimization Problems with Set-Valued Maps

DOI10.1080/01630560903499845zbMath1218.90163OpenAlexW1975718111MaRDI QIDQ3578000

Le Anh Tuan

Publication date: 13 July 2010

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

Full work available at URL: https://doi.org/10.1080/01630560903499845

zbMATH Keywords

vector optimization problemset-valued map\(\varepsilon \)-efficient solution\(\varepsilon \)-Benson proper efficient solution\(\varepsilon \)-Benson proper subdifferentials\(\varepsilon \)-Benson proper subgradient\(\varepsilon \)-optimality condition\(\varepsilon \)-subgradient

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Multi-objective and goal programming (90C29) Optimality conditions and duality in mathematical programming (90C46)

Related Items (13)

A kind of unified super efficiency via assumption (A) and applications in vector optimization ⋮ Sequential \(\varepsilon\)-subdifferential calculus for scalar and vector mappings ⋮ Sequential characterizations of approximate solutions in convex vector optimization problems with set-valued maps ⋮ Approximate quasi efficiency of set-valued optimization problems via weak subdifferential ⋮ Chain rules for a proper \(\varepsilon\)-subdifferential of vector mappings ⋮ \(\varepsilon\)-strict subdifferentials of set-valued maps and optimality conditions ⋮ \(E\)-super efficiency of set-valued optimization problems involving improvement sets ⋮ Unnamed Item ⋮ \(\epsilon\)-optimality conditions of vector optimization problems with set-valued maps based on the algebraic interior in real linear spaces ⋮ Scalarization of \(\epsilon\)-super efficient solutions of set-valued optimization problems in real ordered linear spaces ⋮ Subdifferential calculus for set-valued mappings and optimality conditions for multiobjective optimization problems ⋮ Approximate duality for vector quasi-equilibrium problems and applications ⋮ Scalarization and saddle points of approximate proper solutions in nearly subconvexlike vector optimization problems

Cites Work

• Unnamed Item
• Nearly subconvexlike set-valued maps and vector optimization problems
• Moreau-Rockafellar theorems for nonconvex set-valued maps
• \(\varepsilon \)-optimality and \(\varepsilon \)-Lagrangian duality for a nonconvex programming problem with an infinite number of constraints
• \(\epsilon\)-solutions in vector minimization problems
• \(\varepsilon\)-optimality criteria for convex programming problems via exact penalty functions
• On subdifferentials of set-valued maps
• Optimality conditions for set-valued optimization problems
• A characterization of proper minimal points as solutions of sublinear optimization problems
• Contingent epiderivatives and set-valued optimization
• Optimality conditions in non-convex set-valued optimization
• \(K\)-epiderivatives for set-valued functions and optimization
• Near-subconvexlikeness in vector optimization with set-valued functions
• New generalized convexity notion for set-valued maps and application to vector optimization
• On set-valued optimization.
• Characterizing global optimality for DC optimization problems under convex inequality constraints
• Duality results for generalized vector variational inequalities with set-valued maps
• \(\varepsilon\)-subdifferentials of set-valued maps and \(\varepsilon\)-weak Pareto optimality for multiobjective optimization
• Strong Duality with Proper Efficiency in Multiobjective Optimization Involving Nonconvex Set-Valued Maps
• ε-Optimal solutions in nondifferentiable convex programming and some related questions
• The Lagrange Multiplier Rule in Set-Valued Optimization
• Weak Subdifferential of Set-Valued Mappings
• Subdifferential calculus without qualification conditions, using approximate subdifferentials: A survey
• e-weak minimal solutions of vector optimization problems with set-valued maps

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