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Smoothing Newton Methods for Sloving e1 Norm Optimization Model

Author: JiaHongTao
Tutor: ZhangHongWei
School: Dalian University of Technology
Course: Operational Research and Cybernetics
Keywords: e1 norm Second-order cone constraints Smoothing Newton Method Global Convergence Local quadratic convergence
CLC: O224
Type: Master's thesis
Year: 2010
Downloads: 22
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Abstract


In engineering applications , usually with multiple features of an object composed of high - dimensional vector to describe the objects . Linear normed space , the similarity between objects are often characterized by the l1 norm of the difference vector . The face recognition system , for example , the facial features of the people by the high -dimensional vector to represent , and then build the l1 norm optimization model was solved to achieve the purpose of face recognition . So the l1 norm optimization model for solving becomes an important issue . This paper studies a class of linear constraints l1 norm optimization problem . Through the introduction of the second-order cone constraints , the objective function can be transformed into smooth function which the original problem into a second order cone constrained optimization problem . Convenience, in order to study the original problem was constructed based on duality theory the dual problem , then the dual problem is solved . In the solution process , the introduction of the Fischer-Burmeister function complementary KKT system conditions to equivalent replacement will have the dual problem KKT system into a non - smooth equations and then with Armijo line search of the smoothing Newton method for solving . We to verify JΦ the non - singularity , the global and local quadratic convergence properties of the algorithm . Finally, write a MATLAB program for numerical solution .

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CLC: > Mathematical sciences and chemical > Mathematics > Operations Research > Optimization of the mathematical theory
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