The Natures Of Strong Quasiconcave Function And Its Apply In Utility Function

It's difficult to value a plan by only one objective function, according to the real station in live and production. Usually it needs several objections which mutually affects even opposed to each other. Multi-objective optimization is a new branch of subjects studying more than one objects'programming. It is widely used in some area, such as System science, Economic planning, Energy development ,Military science and so on. All of these applications are rationally studied by building Mathematical models. Concave and convex functions with their natures form the theory basis and useful tools for the studying of Mathematical programming, Variation, multi-objective programming. but it barely give the applications of Strong quasiconcave functions here.This article first states the present and development situations of multi-objective optimization, discussing its objective and constraint functions but their natures. it summaries the relationgships between each, and gives us two natures of strong quasiconcave functions, the results of which under control of some conditions. The last part of the article gives the applying of strong quasiconcave functions in Utility theory, assuming that the consumer's utility functions are strong quasiconcave. We can get many results about these functions by studying the theory and characteristics. Actually we can abundantly use them in Social production.