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The Study of Properties and Algorithm for Several Classes of No-linear Convex Programming

Author: ZouLaYing
Tutor: YeXiangQi
School: Jiangxi Normal University
Course: Applied Mathematics
Keywords: Convex programming Quadratic Programming Bilevel programming Complementary shaft Law K-T conditions Frank-Wolf method
CLC: O221.2
Type: Master's thesis
Year: 2008
Downloads: 75
Quote: 0
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Abstract


This article is about the nature of the three types of convex programming and algorithm research paper is divided into two chapters introduce these three categories convex planning , previous layer of convex quadratic programming , after a chapter on the second floor planning ; their algorithm KT conditions common is the use of the transformation model . innovation of this paper are two : 1 . simplex method solution to the upper and lower constrained Layer 2 linear convex planning , which is reflected in the 3.2 ; Frank-Wolfe algorithm to solve the upper for solving nonlinear Layer 2 convex programming , which was reflected in a 3.3 . Chapter prior knowledge ; The second chapter describes the nature of the convex quadratic programming and algorithms , KT conditions on the basis of the research on the nature of the convex quadratic programming convex quadratic programming transformation , then take advantage of the complementary shaft method to solve convex quadratic programming ; Chapter is convex bilevel programming , earlier in this chapter a linear bilevel programming nature and algorithms , using the KT conditions on the study of the nature of the model is transformed , then equilibrium point is obtained by the simplex method to solve the model ; behind a non-linear bilevel programming , linear programming , it is the first layer of the objective function is convex quadratic function , the model is transformed by KT conditions , then Frank-Wolf linear approximation method to solve .

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