Continuity of the solutions sets for parametric set optimization problems

Abstract

Abstract The current study focuses on exploring the stability of solution sets pertaining to set optimization problems, particularly with regard to the set order relation outlined by Karaman et al. 2018. Sufficient conditions are provided for the lower semicontinuity, upper semicontinuity, and compactness of m-minimal solution mappings in parametric set optimization, where the involved set-valued mapping is Lipschitz continuous.

Keywords

• Set optimization
• Stability
• Semicontinuity
• Locally Lipschitz continuity