Quasi-Optimization Problems: Existence, Iterative Algorithms and Well-Posedness

The aim of this article is to introduce and study a quasi-optimization problem (QOP, for short) on an infinite dimensional Banach space. First, under mild assumptions, we deliver three existence theorems for (QOP) by employing Kluge's fixed point principle for multivalued operators. Then, several sufficient and necessary conditions for a solution of (QOP) are proved. Furthermore, two iterative algorithms are proposed and the convergence results are obtained. Finally, the well-posedness and generalized well-posedness of (QOP) are introduced and its equivalent metric characteristic is established.