EXISTENCE OF SOLUTIONS OF ORDERED SET QUASI-OPTIMIZATION PROBLEMS

In this paper, we consider ordered set optimization problems in scenarios where preferences are given by arbitrary pre-order. If the constrained set depends on the solution itself, then such problems are called ordered set quasi-optimization problems. By using fixed point theorems, we establish existence results for solutions of ordered set quasi-optimization problems as well as ordered set optimization problems. Such results can be treated as a generalization of Weierstrass minimizing theorem to set-valued mappings. The results of this paper either generalize known results and completely new in the literature.