A Global Optimization Algorithm for Sum of Linear Ratios Problem

被引：21

作者：

Gao, Yuelin ^{[1
]}

Jin, Siqiao ^{[1
]}

机构：

[1] Beifang Univ Nationalities, Inst Informat & Syst Sci, Yinchuan 750021, Peoples R China

来源：

JOURNAL OF APPLIED MATHEMATICS | 2013年

关键词：

D O I：

10.1155/2013/276245

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.

引用

页数：7

共 10 条

[1]

[Anonymous], NONCONVEX OPTIMIZATI

[2] Solving sum of ratios fractional programs via concave minimization [J].

Benson, H. P. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2007, 135 (01) :1-17

[3] A global optimization algorithm for linear fractional programming [J].

Chun-Feng, Wang ;

Pei-Ping, Shen .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 204 (01) :281-287

[4]

Falk J., 1992, RECENT ADV GLOBAL OP, P221

[5] Global Optimization for Sum of Linear Ratios Problem Using New Pruning Technique [J].

Jiao, Hongwei ;

Feng, Qigao ;

Shen, Peiping ;

Guo, Yunrui .

MATHEMATICAL PROBLEMS IN ENGINEERING, 2008, 2008

[6] Bond portfolio optimization problems and their applications to index tracking: A partial optimization approach [J].

Konno, H ;

Watanabe, H .

JOURNAL OF THE OPERATIONS RESEARCH SOCIETY OF JAPAN, 1996, 39 (03) :295-306

[7] Minimization of the sum of three linear fractional functions [J].

Konno, H ;

Abe, N .

JOURNAL OF GLOBAL OPTIMIZATION, 1999, 15 (04) :419-432

[8]

Konno H., 1991, J. Global Optim., V1, P65, DOI DOI 10.1007/BF00120666

[9] Global optimization for sum of linear ratios problem with coefficients [J].

Shen, PP ;

Wang, CF .

APPLIED MATHEMATICS AND COMPUTATION, 2006, 176 (01) :219-229

[10] A branch-and-bound algorithm to globally solve the sum of several linear ratios [J].

Wang, YJ ;

Shen, PP ;

Liang, Z .

APPLIED MATHEMATICS AND COMPUTATION, 2005, 168 (01) :89-101

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