Improvement sets and vector optimization

DOI10.1016/j.ejor.2012.05.050zbMath1292.90268OpenAlexW2005341901MaRDI QIDQ2253346

Bienvenido Jiménez, Vicente Novo Sanjurjo, César Gutiérrez

Publication date: 27 July 2014

Published in: European Journal of Operational Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ejor.2012.05.050

zbMATH Keywords

vector optimizationscalarizationimprovement setminimal point\(\epsilon\)-efficiency

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Set-valued and variational analysis (49J53)

Related Items (42)

A kind of unified super efficiency via assumption (A) and applications in vector optimization ⋮ Density and connectedness of optimal points with respect to improvement sets ⋮ Characterizations of improvement sets via quasi interior and applications in vector optimization ⋮ Unified vector quasiequilibrium problems via improvement sets and nonlinear scalarization with stability analysis ⋮ Painlevé-Kuratowski convergence of minimal solutions for set-valued optimization problems via improvement sets ⋮ The stability of minimal solution sets for set optimization problems via improvement sets ⋮ Further results on quasi efficient solutions in multiobjective optimization ⋮ A kind of unified strict efficiency via improvement sets in vector optimization ⋮ Some saddle-point theorems for vector-valued functions ⋮ Existence of optimal points via improvement sets ⋮ Properties of the nonlinear scalar functional and its applications to vector optimization problems ⋮ \(E\)-super efficiency of set-valued optimization problems involving improvement sets ⋮ Stability of optimal points with respect to improvement sets ⋮ Conic scalarizations for approximate efficient solutions in nonconvex vector optimization problems ⋮ Technical note on the existence of solutions for generalized symmetric set-valued quasi-equilibrium problems utilizing improvement set ⋮ Ekeland Variational Principles in Vector Equilibrium Problems ⋮ Continuity of the solution set mappings for parametric unified weak quasivariational inequalities via free-disposal set mappings ⋮ Scalarization in vector optimization with arbitrary domination sets ⋮ A kind of unified proper efficiency in vector optimization ⋮ Separations and optimality of constrained multiobjective optimization via improvement sets ⋮ A unified concept of approximate and quasi efficient solutions and associated subdifferentials in multiobjective optimization ⋮ Stability and scalarization in vector optimization using improvement sets ⋮ Vector optimization using improvement sets in locally convex spaces ⋮ Nonlinear separation concerning \(E\)-optimal solution of constrained multi-objective optimization problems ⋮ Approximate solutions of vector optimization problems via improvement sets in real linear spaces ⋮ Nonlinear separation methods and applications for vector equilibrium problems using improvement sets ⋮ Unifying local-global type properties in vector optimization ⋮ Characterizing efficiency on infinite-dimensional commodity spaces with ordering cones having possibly empty interior ⋮ A scalarization scheme for binary relations with applications to set-valued and robust optimization ⋮ Scalarizations and optimality of constrained set-valued optimization using improvement sets and image space analysis ⋮ Some properties of nonconvex oriented distance function and applications to vector optimization problems ⋮ On Hadamard well-posedness of families of Pareto optimization problems ⋮ Approximate proper efficiency in vector optimization ⋮ Existence and Convergence of Optimal Points with Respect to Improvement Sets ⋮ Vectorial form of Ekeland variational principle with applications to vector equilibrium problems ⋮ Vector equilibrium problems under improvement sets and linear scalarization with stability applications ⋮ The connectedness of the solutions set for set-valued vector equilibrium problems under improvement sets ⋮ The stability of the solution sets for set optimization problems via improvement sets ⋮ Nonconvex Separation Functional in Linear Spaces with Applications to Vector Equilibria ⋮ A characterization of \(E\)-Benson proper efficiency via nonlinear scalarization in vector optimization ⋮ Improvement sets and convergence of optimal points ⋮ Optimality conditions for quasi-solutions of vector optimization problems

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