On Optimization Problems in Quasi-Metric Spaces

This paper is concerned with optimization problems in quasi-metric spaces. Many optimization problems such as vector optimization, set-valued optimization, are unified in the quasi-metric space to have a simple expression. In this paper, optimization problems in quasi-metric spaces are put forward firstly, and then the conclusion that infimum of a lower semi-continuous mapping from a compact set to a quasi-metric space can be reached is received. Subsequently, the proposition that there exists an order cone at lest in each asymmetric norm space is proved. In the end, the conclusion is drawn, which an asymmetric norm is determined by a Banach space and an order cone