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A Smoothing Method for an Inverse Linear Programming Problem

Author: HuangWan
Tutor: ZhangLiWei
School: Dalian University of Technology
Course: Operational Research and Cybernetics
Keywords: Inverse linear programming problem l_ ∞ norm Maximum entropy method F-B function Newton Quadratic
CLC: O221.1
Type: Master's thesis
Year: 2010
Downloads: 46
Quote: 0
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Abstract


Inverse optimization problems in various fields has wide application value , so in recent years it has gradually become a hot research scholars at home and abroad . About the inverse problem of linear programming research results will be more, but for the l ∞ norm of the inverse problem of linear programming effective algorithm is rare . For this reason, this paper, a class of l ∞ norm of the inverse problem of linear programming numerical algorithms are studied. This inverse problem as small as possible to adjust through linear programming problems the objective function parameters so that a known feasible solution is adjusted to the optimal solution . In this paper we use this inverse problem is transformed into a class of equality constrained optimization problem, and use Newton's method to solve them . The main contents of this paper can be summarized as follows: 1, the first chapter introduces the research background and inverse problem situation , and then put forward in this paper to study a class of l ∞ norm of the inverse problem of linear programming problems . 2, the second chapter is mainly constrained optimization problem given some basic knowledge , these results are transformed inverse problem and convergence analysis of need. 3 , in the third chapter, we use the maximum entropy method and the Fischer-Burmeister smoothing function problems and prove the optimal solution perturbations converge to the optimal solution of the original problem . Since the problem is perturbed equation containing only a constrained nonlinear programming problem , and its KKT conditions can be expressed with a smooth equations , so we give its KKT condition , and proved Jacobin matrix of non- singular . 4 , the fourth chapter , gives a solution of the perturbed problem Newton algorithm and prove global and local second-order algorithm convergence . 5 , the fifth chapter , the algorithm is given numerical experiments verify the effectiveness of the algorithm .

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