A generic approach to approximate efficiency and applications to vector optimization with set-valued maps

DOI10.1007/s10898-010-9546-4zbMath1239.90092OpenAlexW2069426380MaRDI QIDQ625654

Vicente Novo Sanjurjo, César Gutiérrez, Bienvenido Jiménez

Publication date: 25 February 2011

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10898-010-9546-4

zbMATH Keywords

vector optimizationexistence theoremPainlevé-Kuratowski convergencepoint-to-set mapping\(\varepsilon \)-efficient point

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Approximation methods and heuristics in mathematical programming (90C59)

Related Items (12)

Approximate quasi efficiency of set-valued optimization problems via weak subdifferential ⋮ Further results on quasi efficient solutions in multiobjective optimization ⋮ Approximate weak minimal solutions of set-valued optimization problems ⋮ Approximation of Weak Efficient Solutions in Vector Optimization ⋮ Duality related to approximate proper solutions of vector optimization problems ⋮ Vector optimization problems via improvement sets ⋮ \(\epsilon\)-optimality conditions of vector optimization problems with set-valued maps based on the algebraic interior in real linear spaces ⋮ Stability and scalarization in vector optimization using improvement sets ⋮ Improvement sets and vector optimization ⋮ Scalarization approach for approximation of weakly efficient solutions of set-valued optimization problems ⋮ Limit Behavior of Approximate Proper Solutions in Vector Optimization ⋮ Generalized \({\varepsilon }\)-quasi solutions of set optimization problems

Cites Work

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• On approximate efficiency in multiobjective programming
• On approximate solutions in vector optimization problems via scalarization
• Well posedness in vector optimization problems and vector variational inequalities
• Optimality conditions via scalarization for a new \(\epsilon \)-efficiency concept in vector optimization problems
• Theory of multiobjective optimization
• Epsilon efficiency
• On two generalizations of Pareto minimality
• Ekeland's \(\varepsilon\)-variational principle for set-valued mappings
• On several concepts for \(\varepsilon\)-efficiency
• General Ekeland's variational principle for set-valued mappings.
• \(\varepsilon\)-optimality for multiobjective programming on a Banach space
• On variational principles, level sets, well-posedness, and \(\epsilon\)-solutions in vector optimization
• On the existence and stability of approximate solutions of perturbed vector equilibrium problems
• A survey of recent developments in multiobjective optimization
• Optimality conditions for metrically consistent approximate solutions in vector optimization
• Multiplier rules and saddle-point theorems for Helbig's approximate solutions in convex Pareto problems
• ON APPROXIMATE MINIMA IN VECTOR OPTIMIZATION
• A Set-Valued Ekeland's Variational Principle in Vector Optimization
• On Approximate Solutions in Convex Vector Optimization
• A nonconvex vector minimization problem
• Between Pareto efficiency and Pareto ε-efficiency
• A Unified Approach and Optimality Conditions for Approximate Solutions of Vector Optimization Problems
• e-weak minimal solutions of vector optimization problems with set-valued maps
• Characterizing properties of approximate solutions for optimization problems

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