Connectedness of the approximate solution sets for set optimization problems
Yu Han
Abstract
In this paper, we deal with connectedness of the approximate solution sets for set optimization problems by using the scalarization method. We first obtain two scalarization results for the sets of l-minimal approximate solutions and weak l-minimal approximate solutions for set optimization problems without using the convexity of the objective mapping and the separation theorem of convex sets. Then, we establish connectedness of the sets of l-minimal approximate solutions and weak l-minimal approximate solutions for set optimization problems by utilizing the scalarization results. Finally, we derive arcwise connectedness of the set of weak l-minimal approximate solutions for set optimization problems.
Topics & Concepts
Social connectednessMathematicsConvexitySolution setSet (abstract data type)Optimization problemRegular polygonMathematical optimizationApplied mathematicsDiscrete mathematicsCombinatoricsComputer scienceGeometryFinancial economicsProgramming languagePsychologyPsychotherapistEconomicsOptimization and Variational AnalysisAdvanced Optimization Algorithms ResearchOptimization and Mathematical Programming