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The New Line Search Technique And Its Application In Drop Method

Posted on:2013-09-08Degree:MasterType:Thesis
Country:ChinaCandidate:X D ZhengFull Text:PDF
GTID:2240330374488314Subject:Operational Research and Cybernetics
Abstract/Summary:PDF Full Text Request
Line search technique for solving unconstrained problems is hot and difficult in the field of management science and engineering, operation reseach, and decision science research. In the field of engineering and economic management, it has a strong research background and has made great progress recently. In this paper, on the basis of existing research, we proposed several new highly efficient line search techniques, and studied their applications in decent method.Firstly, we introduced several classical line search techniques and decent algorithms. After giving a review on the recent advances, we also summarized the main work in this paper.Secondly, motivated by the classical Armijo-type line search and the Wolfe-type line search, we proposed a new hybrid line search technique which was designed to improve the efficiency of line search. Based on this new line search strategy, Newton algorithm was developed to solve the unconstrained optimization problems. Under some mild assumptions, the global convergence theorem of this algorithm was proved. Numerical experiments showed that our proposed line search technique was a kind of effective methods.Thirdly, we proposed a modified Armijo-type line search rule. Then, on the basis of this line search, a new cautious BFGS algorithm was developed. It would be shown that in our line search, a larger descent magnitude of objective function was obtained with lower cost of computation at every iteration. In addition, the initial step size was adjusted automatically at each iteration. Under some mild assumptions, the global convergence of the algorithm was established for nonconvex optimization problems. Numerical results demonstrated that the proposed method was promising, especially in comparison with the existing method.Finally, a new inexact line search rule was presented, which was a modified version of the standard Armijo line search rule by incorporating the information of the second order derivative of objective function. By new line search, large descent magnitude of objective function was obtained with relatively lower cost of computation at every iteration. In addition, the initial step size in the new line search was adjusted automatically at each iteration, which was related to the improvement of numerical behavior. With this line search, a class of descent algorithms were developed. Under some mild assumptions, the global convergence of these algorithms was established for solving unconstrained optimization problems. Numerical results demonstrated that the proposed method was promising.
Keywords/Search Tags:unconstrained optimization, global convergence, linesearch technique, steep decent method, Newton method, BFGS
PDF Full Text Request
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