Variable programming: A generalized minimax problem. Part II: Algorithms
Publication in refereed journal

香港中文大學研究人員

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摘要In this part of the two-part series of papers, algorithms for solving some variable programming (VP) problems proposed in Part I are investigated. It is demonstrated that the non-differentiability and the discontinuity of the maximum objective function, as well as the summation objective function in the VP problems constitute difficulty in finding their solutions. Based on the principle of statistical mechanics, we derive smooth functions to approximate these non-smooth objective functions with specific activated feasible sets. By transforming the minimax problem and the corresponding variable programming problems into their smooth versions we can solve the resulting problems by some efficient algorithms for smooth functions. Relevant theoretical underpinnings about the smoothing techniques are established. The algorithms, in which the minimization of the smooth functions is carried out by the standard quasi-Newton method with BFGS formula, are tested on some standard minimax and variable programming problems. The numerical results show that the smoothing techniques yield accurate optimal solutions and that the algorithms proposed are feasible and efficient.
著者Jiao YC, Leung Y, Xu ZB, Zhang JS
期刊名稱Computational Optimization and Applications
出版年份2005
月份3
日期1
卷號30
期次3
出版社SPRINGER
頁次263 - 295
國際標準期刊號0926-6003
電子國際標準期刊號1573-2894
語言英式英語
關鍵詞minimax; smooth optimization; statistical mechanics principle; variable programming
Web of Science 學科類別Mathematics; Mathematics, Applied; MATHEMATICS, APPLIED; Operations Research & Management Science; OPERATIONS RESEARCH & MANAGEMENT SCIENCE

上次更新時間 2020-13-10 於 01:25