Stability analysis for set-valued optimization in Geoffroy spaces

2025/03/05 by Larrouy, James
#49J53 #54A20 #65K10 #90C29 #90C31 #FOS: Mathematics #General Topology (math.GN) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2503.03405

Abstract

In this work, we study the external and internal stability of minimal solutions to set-valued optimization problems in a new functional framework. We consider perturbations on both the objective function and the admissible domain. To address these problems, we introduce two variational convergences for sequences of set-valued maps, namely the Gamma-cone convergence and the sequential Gamma-cone convergence. The upper and the lower convergence of strong level sets are also studied.

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