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The Research on the Algorithms of Some Quadratic Programming

Author: ShengGuiYing
Tutor: GaoLeiFu
School: Liaoning Technical University
Course: Applied Mathematics
Keywords: Quadratic Programming Convex Quadratic Programming Lemke algorithm Newton interior point algorithm Linear complementarity problems Algorithm
CLC: O221.2
Type: Master's thesis
Year: 2009
Downloads: 220
Quote: 0
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Abstract


In this thesis, some quadratic programming algorithm is studied , analyzed some common quadratic programming algorithm limitations, while improving both algorithms and numerical experiments verified using MATLAB algorithm. Thesis introduces the basics of quadratic programming , based on some commonly used algorithms are described and analyzed , focusing introduced and analyzed Lemke complementary pivot algorithm and Newton interior point algorithm . Analysis of the advantages and disadvantages of correlation algorithm , through the classic Lemke complementary pivot algorithm for convex quadratic programming problem analysis, found Lemke algorithm limitations. Meanwhile, Newton interior point algorithm found inadequacies in order to improve it. Convex Quadratic Programming thesis according to Lemke algorithm described Lemke gives an improved algorithm to solve without introducing artificial variables , and gives specific steps to improve the algorithm and the improved algorithm is tested on specific examples . By using improved Lemke algorithm convex quadratic programming problems , the improved algorithm with the classic Lemke algorithm to do the comparison and analysis, the improved algorithm. Numerical results show that the improved algorithm is correct , and to reduce the convex quadratic programming problem iterative process. Papers while Newton interior point algorithm is proposed to improve the solving convex quadratic programming problems new algorithms. This algorithm is put on the number of penalty function method and quasi-Newton algorithm is an effective combination , the constraint problem into an unconstrained problem, using Wolf-Powell line search to determine step length , avoiding the search step too small problem . Quasi-Newton algorithm using the optimal solution , and the algorithm convergence analysis . Finally, preliminary numerical results show that the algorithm is feasible and effective .

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