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Paper IPM / M / 15495  


Abstract:  
In this paper, we introduce the notion of generalized Levitinï¿½??Polyak (in short gLP) wellposedness for set optimization problems. We provide some characterizations of gLP wellposedness in terms of the upper Hausdorff convergence and PainlevÃ©ï¿½??Kuratowski convergence of a sequence of sets of approximate solutions, and in terms of the upper semicontinuity and closedness of an approximate solution map. We obtain some equivalence relationships between the gLP wellposedness of a set optimization problem and the gLP wellposedness of two corresponding scalar optimization problems. Also, we give some other characterizations of gLP wellposedness by two extended forcing functions and the Kuratowski noncompactness measure of the set of approximate solutions. Finally we show that certain conesemicontinuous and conequasiconvex set optimization problems are gLP wellposed.
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