A unified vector optimization problem: complete scalarizations and applications

DOI10.1080/02331934.2011.641018zbMath1266.90162OpenAlexW2006066505MaRDI QIDQ3111143

Elvira Hernández, Fabián Flores-Bazan

Publication date: 18 January 2012

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331934.2011.641018

zbMATH Keywords

vector optimization problemsefficiencyweak efficiencystrict efficiencyapproximate efficiencycomplete scalarizationsoptimaliy conditions

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Multi-objective and goal programming (90C29) Nonlinear programming (90C30) Optimality conditions and duality in mathematical programming (90C46)

Related Items (36)

A kind of unified super efficiency via assumption (A) and applications in vector optimization ⋮ First and second order optimality conditions in vector optimization problems with nontransitive preference relation ⋮ Conditions for solutions, their globality, and their duality relations in vector optimization with relaxed quasiconvexity ⋮ Quadratic scalarization for decomposed multiobjective optimization ⋮ Efficiency in quasiconvex multiobjective nondifferentiable optimization on the real line ⋮ Optimality conditions for a unified vector optimization problem with not necessarily preordering relations ⋮ Characterizing ϵ-properly efficient solutions ⋮ Convergence of relaxed minimizers in set optimization ⋮ Proper or weak efficiency via saddle point conditions in cone-constrained nonconvex vector optimization problems ⋮ Further results on quasi efficient solutions in multiobjective optimization ⋮ Existence of optimal points via improvement sets ⋮ A unified minimal solution in set optimization ⋮ Stability in unified semi-infinite vector optimization ⋮ Conic scalarizations for approximate efficient solutions in nonconvex vector optimization problems ⋮ Метод множителей Лагранжа в классе субгладких отображений ⋮ Scalarization in vector optimization with arbitrary domination sets ⋮ A kind of unified proper efficiency in vector optimization ⋮ Notes on Lipschitz properties of nonlinear scalarization functions with applications ⋮ Optimality conditions and minimax properties in set optimization ⋮ Continuity and closedness of constraint and solution set mappings in unified parametric semi-infinite vector optimization ⋮ Scalarizations for a unified vector optimization problem based on order representing and order preserving properties ⋮ Unifying local-global type properties in vector optimization ⋮ Characterizing efficiency on infinite-dimensional commodity spaces with ordering cones having possibly empty interior ⋮ Characterizations of efficient and weakly efficient points in nonconvex vector optimization ⋮ Comparison of some scalarization methods in multiobjective optimization ⋮ Ekeland variational principles involving set perturbations in vector equilibrium problems ⋮ Essential stability in unified vector optimization ⋮ A Survey of Set Optimization Problems with Set Solutions ⋮ Approximate proper efficiency in vector optimization ⋮ Stability and scalarization for a unified vector optimization problem ⋮ Optimality conditions via a unified direction approach for (approximate) efficiency in multiobjective optimization ⋮ E-Benson proper efficiency in vector optimization ⋮ Nonconvex Separation Functional in Linear Spaces with Applications to Vector Equilibria ⋮ A characterization of \(E\)-Benson proper efficiency via nonlinear scalarization in vector optimization ⋮ Existence and characterization theorems in nonconvex vector optimization ⋮ Optimality conditions for quasi-solutions of vector optimization problems

Cites Work

• Unnamed Item
• Scalarization and nonlinear scalar duality for vector optimization with preferences that are not necessarily a pre-order relation
• Nonconvex separation theorems and some applications in vector optimization
• Nonconvex scalarization in set optimization with set-valued maps
• Generating \(\varepsilon\)-efficient solutions in multiobjective programming
• On approximate solutions in vector optimization problems via scalarization
• On the characterization of efficient production vectors
• Some properties of approximate solutions for vector optimization problem with set-valued functions
• An optimal alternative theorem and applications to mathematical programming
• Optimality conditions via scalarization for a new \(\epsilon \)-efficiency concept in vector optimization problems
• Epsilon efficiency
• Existence of equilibria when firms follow bounded losses pricing rules
• New optimality principles for economic efficiency and equilibrium
• A solvability theorem for a class of quasiconvex mappings with applications to optimization
• Variational methods in partially ordered spaces
• Scalarizing vector optimization problems
• Semistrictly quasiconvex mappings and non-convex vector optimization
• On the choice of parameters for the weighting method in vector optimization
• Scalarization in vector optimization
• Lipschitz properties of the scalarization function and applications
• Strict Efficiency in Set-Valued Optimization
• Fuzzy necessary optimality conditions for vector optimization problems
• SUBLINEAR OPERATORS AND THEIR APPLICATIONS
• A Unified Approach and Optimality Conditions for Approximate Solutions of Vector Optimization Problems

This page was built for publication: A unified vector optimization problem: complete scalarizations and applications