Nonconvex scalarization in set optimization with set-valued maps
From MaRDI portal
Publication:854022
DOI10.1016/j.jmaa.2006.01.033zbMath1110.90080OpenAlexW2035990529MaRDI QIDQ854022
Luis Rodríguez-Marín, Elvira Hernández
Publication date: 7 December 2006
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.01.033
optimality conditionsset-valued optimizationset optimizationGerstewitz's nonconvex separation functionalnonconvex scalarization
Related Items (only showing first 100 items - show all)
Well-posedness for the optimistic counterpart of uncertain vector optimization problems ⋮ Applying set optimization to weak efficiency ⋮ Set optimization problems of generalized semi-continuous set-valued maps with applications ⋮ Existence theorems for set optimization problems ⋮ On the ordinal structure of the weighted set relation ⋮ Some properties of generalized oriented distance function and their applications to set optimization problems ⋮ Characterizations of the set less order relation in nonconvex set optimization ⋮ On the stability of the solution set mappings to parametric set optimization problems ⋮ Convergence of solutions of a set optimization problem in the image space ⋮ On the solution continuity of parametric set optimization problems ⋮ \((\Lambda ,C)\)-contingent derivatives of set-valued maps ⋮ Optimality conditions for a unified vector optimization problem with not necessarily preordering relations ⋮ New scalarizing approach to the stability analysis in parametric generalized Ky Fan inequality problems ⋮ About Hahn-Banach extension theorems and applications to set-valued optimization ⋮ Generalized Hukuhara Gâteaux and Fréchet derivatives of interval-valued functions and their application in optimization with interval-valued functions ⋮ Generalized \(B\)-well-posedness for set optimization problems ⋮ Continuity and convexity of a nonlinear scalarizing function in set optimization problems with applications ⋮ Connectedness of weak minimal solution set for set optimization problems ⋮ Partial order relations on family of sets and scalarizations for set optimization ⋮ Semicontinuity property of approximate solution mappings in bifunction-set optimization ⋮ Strict approximate solutions in set-valued optimization with applications to the approximate Ekeland variational principle ⋮ Convergence of solutions to set optimization problems with the set less order relation ⋮ Continuity of solution mappings in some parametric non-weak vector Ky Fan inequalities ⋮ Continuity of cone-convex functions ⋮ On solutions of set-valued optimization problems ⋮ Pointwise well-posedness and scalarization in set optimization ⋮ Some minimax theorems of set-valued maps and their applications ⋮ Lagrange multipliers in convex set optimization with the set and vector criteria ⋮ Characterizations of set order relations and nonlinear scalarizations via generalized oriented distance function in set optimization ⋮ Locating minimal sets using polyhedral cones ⋮ Weak sharp minima in set-valued optimization problems ⋮ A unified minimal solution in set optimization ⋮ Pointwise well-posedness in set optimization with cone proper sets ⋮ Four types of nonlinear scalarizations and some applications in set optimization ⋮ Global well-posedness of set-valued optimization with application to uncertain problems ⋮ Directional derivatives and subdifferentials for set-valued maps applied to set optimization ⋮ Optimality conditions in set-valued optimization problem with respect to a partial order relation via directional derivative ⋮ Existence of solutions of a generalized bifunction-set optimization problem ⋮ Pointwise well-posedness of a set-valued optimization problem at a weak solution ⋮ On optimization problems with set-valued objective maps: existence and optimality ⋮ On essential stable sets of solutions in set optimization problems ⋮ Solution existence in bifunction-set optimization ⋮ On approximate solutions in set-valued optimization problems ⋮ A calculation approach to scalarization for polyhedral sets by means of set relations ⋮ Solving set optimization problems based on the concept of null set ⋮ Lagrangian duality in set-valued optimization ⋮ Continuity of the solution set mappings to a parametric set optimization problem ⋮ Pointwise and global well-posedness in set optimization: a direct approach ⋮ Characterizing efficiency without linear structure: a unified approach ⋮ Second-order optimality conditions for set optimization using coradiant sets ⋮ Optimality conditions and minimax properties in set optimization ⋮ Set relations and weak minimal solutions for nonconvex set optimization problems with applications ⋮ Variational inequalities characterizing weak minimality in set optimization ⋮ Stability and scalarization in vector optimization using improvement sets ⋮ Scalarization and pointwise well-posedness for set optimization problems ⋮ Scalarization of multiobjective robust optimization problems ⋮ Qualitative properties of solutions to set optimization problems ⋮ Set approach for set optimization with variable ordering structures. II: Scalarization approaches ⋮ Optimality for set-valued optimization in the sense of vector and set criteria ⋮ Vector optimization using improvement sets in locally convex spaces ⋮ Construction of functions with uniform sublevel sets ⋮ Well-setness and scalarization in set optimization ⋮ Nonlinear scalarization functions and polar cone in set optimization ⋮ Epidifferentiability of the map of infima in Hilbert spaces ⋮ New order relations in set optimization ⋮ Minimax problems for set-valued mappings with set optimization ⋮ Characterizing efficiency on infinite-dimensional commodity spaces with ordering cones having possibly empty interior ⋮ Scalarization in set optimization with solid and nonsolid ordering cones ⋮ Some optimality criteria of interval programming problems ⋮ Weak minimal elements and weak minimal solutions of a nonconvex set-valued optimization problem ⋮ A new nonlinear scalarization function and applications ⋮ Stability property in bifunction-set optimization ⋮ Some equivalent problems in set optimization ⋮ Six set scalarizations based on the oriented distance: continuity, convexity and application to convex set optimization ⋮ Nonlinear Scalarizations of Set Optimization Problems with Set Orderings ⋮ Set Optimization—A Rather Short Introduction ⋮ A Survey of Set Optimization Problems with Set Solutions ⋮ Arcwise connectedness of the solution sets for set optimization problems ⋮ Well-posedness and stability in set optimization with applications ⋮ Optimality conditions for set-valued maps with set optimization ⋮ Characterization of set relations through extensions of the oriented distance ⋮ Ekeland's variational principle with weighted set order relations ⋮ A new concept of slope for set-valued maps and applications in set optimization studied with Kuroiwa's set approach ⋮ The stability and extended well-posedness of the solution sets for set optimization problems via the Painlevé-Kuratowski convergence ⋮ Epidifferentiability and hypodifferentiability of pseudoconvex maps in set-optimization problems ⋮ Well-posedness for set optimization problems ⋮ Scalarization functionals with uniform level sets in set optimization ⋮ Differential stability properties in convex scalar and vector optimization ⋮ Existence of solutions of bifunction-set optimization problems in metric spaces ⋮ A scalarization method for fuzzy set optimization problems ⋮ Well-posedness for set optimization problems involving set order relations ⋮ Continuity of solution maps to parametric set optimization problems via parametric equilibrium problems ⋮ Scalarization and robustness in uncertain vector optimization problems: a non componentwise approach ⋮ Strong vector equilibrium problems with LSC approximate solution mappings ⋮ Scalarizations for a set optimization problem using generalized oriented distance function ⋮ Continuity of solutions mappings of parametric set optimization problems ⋮ New notions of proper efficiency in set optimization with the set criterion ⋮ A derivative-free descent method in set optimization ⋮ Lagrange multipliers, duality, and sensitivity in set-valued convex programming via pointed processes ⋮ Arcwise connected cone-quasiconvex set-valued mappings and Pareto reducibility in vector optimization
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Nonconvex separation theorems and some applications in vector optimization
- Existence and Lagrangian duality for maximization of set-valued functions
- Optimality conditions for set-valued optimization problems
- Nonconvex vector optimization of set-valued mappings.
- Convergence results for weak efficiency in vector optimization problems with equilibrium constraints
- On set-valued optimization.
- Vector network equilibrium problems and nonlinear scalarization methods
- Set-relations and optimality conditions in set-valued maps
- Axiomatic approach to duality in optimization
- Existence theorems of set optimization with set-valued maps
This page was built for publication: Nonconvex scalarization in set optimization with set-valued maps