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The Natures of Strong Quasiconcave Function and Its Apply in Utility Function

Author: CaoRongMei
Tutor: WangQiuTing
School: Wuhan University of Science and Technology
Course: Applied Mathematics
Keywords: Multi-objective optimization Strong Quasiconcave function Utility theory
CLC: O221.6
Type: Master's thesis
Year: 2010
Downloads: 99
Quote: 0
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Abstract


Real production and life , due to an objective situation is more complicated , and sometimes the judge to weigh the pros and cons of a program is difficult to use a goal that required more than one objective measure , these objectives are not that coordinated , and even each other diametrically opposed multi-objective planning is a new branch of the theory and methods of research programming problem with multiple targets, namely multi-objective optimization , its application is very extensive research in the disciplines of systems science and cybernetics as well as economic planning , program management , financial decision-making , energy development , as well as military science and other fields has a large number of applications . these applications almost always require the corresponding mathematical model to rational analysis . convex function and generalized bump is the study of mathematical programming , calculus of variations , optimization theory and other disciplines important theoretical basis and tools but not function Strongly Quasiconcave the practical application of specific manifestation of this paper first introduces the development and current status of the multi-objective optimization problems , the most the objective function and constraint functions convexity of the optimization model and generalized convexity and concavity . summarizes the optimization theory, concave function and generalized concave function of the nature , as well as several concave the function quasiconcave , strict quasiconcave , strong quasiconcave relationship of its proof . on this basis , the study gives strong proposed concave function of the two natures , that is in a semi-continuous conditions meet certain conditions concluded its proof final chapter summarizes the strong proposed concave function in consumer utility theory , utility theory assumes that the consumer's utility function is strong quasiconcave to draw accurately portray the results of consumer behavior , by its nature , used in the production practice .

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CLC: > Mathematical sciences and chemical > Mathematics > Operations Research > Planning Theory ( mathematical programming) > Multiple Objective Programming
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