TITLE:
Continuity of Solution Mappings for Parametric Set Optimization Problems under Partial Order Relations
AUTHORS:
Yueming Sun
KEYWORDS:
Parametric Set Optimization Problem, Nonlinear Scalarization Function, Semicontinuity, Partial Order Relation
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.10 No.11,
November
26,
2020
ABSTRACT: This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.