“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
| Paper IPM / M / 15495 |
|
| Abstract: | |
|
In this paper, we introduce the notion of generalized Levitin�??Polyak (in short gLP) well-posedness for set optimization problems. We provide some characterizations of gLP well-posedness in terms of the upper Hausdorff convergence and Painlev�?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 well-posedness of a set optimization problem and the gLP well-posedness of two corresponding scalar optimization problems. Also, we give some other characterizations of gLP well-posedness by two extended forcing functions and the Kuratowski noncompactness measure of the set of approximate solutions. Finally we show that certain cone-semicontinuous and cone-quasiconvex set optimization problems are gLP well-posed.
Download TeX format |
|
| back to top | |
