A Global Optimization Algorithm for Sum of Linear Ratios Problem

Other literature type, Article English OPEN
Gao, Yuelin ; Jin, Siqiao (2013)
  • Publisher: Hindawi Publishing Corporation
  • Journal: Journal of Applied Mathematics (issn: 1110-757X, eissn: 1687-0042)
  • Related identifiers: doi: 10.1155/2013/276245
  • Subject: Mathematics | QA1-939 | Article Subject

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.
  • References (10)

    Konno, H., Watanabe, H.. Bond portfolio optimization problems and their applications to index tracking: a partial optimization approach. Journal of the Operations Research Society of Japan. 1996; 39 (3): 295-306

    Falk, J. E., Palocsay, S. W.. Optimizing the sum of linear fractional functions. Recent Advances in Global Optimization (Princeton, NJ, 1991). 1992: 221-258

    Horst, R., Pardalos, P. M., Thoai, N. V.. Introduction to Global Optimization. 2000; 48: xiv+353

    Konno, H., Yajima, Y., Matsui, T.. Parametric simplex algorithms for solving a special class of nonconvex minimization problems. Journal of Global Optimization. 1991; 1 (1): 65-81

    Konno, H., Abe, N.. Minimization of the sum of three linear fractional functions. Journal of Global Optimization. 1999; 15 (4): 419-432

    Shen, P.-P., Wang, C.-F.. Global optimization for sum of linear ratios problem with coefficients. Applied Mathematics and Computation. 2006; 176 (1): 219-229

    Yanjun, W., Peiping, S., Zhian, L.. A branch-and-bound algorithm to globally solve the sum of several linear ratios. Applied Mathematics and Computation. 2005; 168 (1): 89-101

    Benson, H. P.. Solving sum of ratios fractional programs via concave minimization. Journal of Optimization Theory and Applications. 2007; 135 (1): 1-17

    Jiao, H. W., Feng, Q. G.. Global optimization for sum of linear ratios problem using new pruning technique. Mathematical Problem in Engineering. 2008; 2008-12

    Wang, C.-F., Shen, P.-P.. A global optimization algorithm for linear fractional programming. Applied Mathematics and Computation. 2008; 204 (1): 281-287

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