Solution Stability and Well-Posedness for Classes of Parametric Set Optimization Problems
Zai-Yun Peng, Yué Zeng, Thái Doãn Chương, Sangwoon Yun, Xin Yang
Abstract
Abstract This paper investigates the solution stability and well-posedness for a parametric set optimization problem (PSOP), where lower and upper set order relations are induced by an improvement set. We provide new sufficient conditions for the outer-continuity, outer-openness and inner-openness of the solution mapping of (PSOP). By utilizing the property of cone-continuity, we derive sufficient conditions ensuring the Levitin-Polyak well-posedness for (PSOP) and the Hadamard well-posedness for a related parametric implicit set optimization problem (ISOP). Numerical examples are also given to illustrate the main results.
Topics & Concepts
MathematicsParametric statisticsTheory of computationMathematical optimizationOptimization problemSet (abstract data type)Stability (learning theory)Solution setHadamard transformParametric programmingProperty (philosophy)Vector optimizationApplied mathematicsNumerical stabilityConstrained optimizationNumerical analysisRandom optimizationOrder (exchange)Multi-objective optimizationSet cover problemStability conditionsFeasible regionFinite setOptimization and Variational AnalysisAdvanced Optimization Algorithms ResearchAdvanced Control Systems Optimization