Global optimization algorithm for a generalized linear multiplicative programming

被引：26

作者：

Jiao, Hongwei ^{[1
,2
]}

Liu, Sanyang ^{[1
]}

Chen, Yongqiang ^{[3
]}

机构：

[1] Department of Mathematical Sciences, Xidian University

[2] Department of Mathematics, Henan Institute of Science and Technology

[3] College of Mathematics and Information, Henan Normal University

来源：

Journal of Applied Mathematics and Computing | 2012年 / 40卷 / 1-2期

基金：

中国国家自然科学基金;

关键词：

Branch and bound algorithm; Deterministic algorithm; Global optimization; Multiplicative programming;

D O I：

10.1007/s12190-012-0576-6

中图分类号：

学科分类号：

摘要：

This article present a branch and bound algorithm for globally solving generalized linear multiplicative programming problems with coefficients. The main computation involve solving a sequence of linear relaxation programming problems, and the algorithm economizes the required computations by conducting the branch and bound search in Rp, rather than in Rn, where p is the number of rank and n is the dimension of decision variables. The proposed algorithm will be convergent to the global optimal solution by means of the subsequent solutions of the series of linear relaxation programming problems. Numerical results are given to show the feasibility and effectiveness of the proposed algorithm. © 2012 Korean Society for Computational and Applied Mathematics.

引用

页码：551 / 568

页数：17

共 37 条

[1]

Konno H., Thach P.T., Tuy H., Optimization on Low Rank Nonconvex Structures, (1997)

[2]

Konno H., Watanabe H., Bond portfolio optimization problems and their applications to index tracking, J. Oper. Res. Soc. Japan, 39, pp. 295-306, (1994)

[3]

Quesada I., Grossmann I.E., Alternative bounding approximations for the global optimization of various engineering design problems, Global Optimization in Engineering Design, pp. 309-331, (1996)

[4]

Maranas C.D., Androulakis I.P., Floudas C.A., Berger A.J., Mulvey J.M., Solving long-term financial planning problems via global optimization, J. Econ. Dyn. Control, 21, pp. 1405-1425, (1997)

[5]

Henderson J.M., Quandt R.E., Microeconomic Theory, (1971)

[6]

Mulvey J.M., Vanderbei R.J., Zenios S.A., Robust optimization of large-scale systems, Oper. Res., 43, pp. 264-281, (1995)

[7]

Matsui T., NP-hardness of linear multiplicative programming and related problems, J. Glob. Optim., 9, pp. 113-119, (1996)

[8]

Konno H., Kuno T., Linear multiplicative programming, Math. Program., 56, pp. 51-64, (1992)

[9]

Swarup H., Programming with indefinite quadratic function with linear constraints, Cah. Centre Etudes Rech. Oper., 8, pp. 223-234, (1966)

[10]

Li H.-M., Zhang K.-C., A decomposition algorithm for solving large-scale quadratic programming problems, Appl. Math. Comput., 173, 1, pp. 394-403, (2006)

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