Optimization Problems In Semi-uniform Spaces

Semi-uniform has been drawing the attentions of domestic and foreign researchers,and its importance in some field has been seen recently.In the paper,some creative basic studies about semi-uniform spaces are carried out,and applications have been implemented in multiple objective optimizations.Currently,the study on the optimization of multiple objective functions is mainly based on orderly Banach spaces,leading to a new uniform theory with wide generalization,moreover,point- ing a new way for the applications of optimal theory in mathematics,cybernetics and economy fields.In this paper, the notion of semi-uniform is put forward, and the proposition that the intersection of all entourages of a semi-uniform is a partial order is testified. Furthermore, the definition and equivalence condition of extremum in the semi-uniform spaces is given by the partial order. After that, the commonly model of optimization problems in the semi-uniform spaces is obtained, and the conclusion that infimum of a lower semi-continuous mapping from a compact set to a semi-uniform space can be reached is received.Finally, one discussed some special case, such as the definition and equivalence condition of real extremum in the semi-uniform spaces. In this way, one could realize the truth of optimization problems in semi-uniform spaces.