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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 72, 2023 - Issue 6
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Articles

A new deterministic global computing algorithm for solving a kind of linear fractional programming

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Pages 1485-1513 | Received 09 Sep 2020, Accepted 10 Nov 2021, Published online: 31 Jan 2022

References

  • Schaible S. Fractional programming. Oper Res. 1976;24(3):452–461.
  • Konno H, Watanabe H. Bond portfolio optimization problems and their applications to index tracking: a partial optimization approach. J Oper Res Soc Jpn. 1996;39(3):295–306.
  • Konno H, Inori M. Bond portfolio optimization by bilinear fractional programming. J Oper Res Soc Jpn. 1989;32(2):143–158.
  • Colantoni CS, Manes RP, Whinston A. Programming, profit rates and pricing decisions. Acc Rev. 1969;44(3):467–481.
  • Sawik B. Downside risk approach for multi-objective portfolio optimization. Oper Res Proc. 2012;2011:191–196.
  • Matsui T. NP-hardness of linear multiplicative programming and related problems. J Glob Optim. 1996;9(2):113–119.
  • Jiao HW, Liu SY. A practicable branch and bound algorithm for sum of linear ratios problem. Eur J Oper Res. 2015;243(3):723–730.
  • Charnes A, Cooper W. Programming with linear fractional functionals. Nav Res Logist. 1962;9(3-4):181–186.
  • Konno H, Yajima Y, Matsui T. Parametric simplex algorithms for solving a special class of nonconvex minimization problems. J Glob Optim. 1991;1:65–81.
  • Carlsson J, Shi J. A linear relaxation algorithm for solving the sum-of-linear-ratios problem with lower dimension. Oper Res Lett. 2013;41(4):381–389.
  • Jiao HW, Liu SY, Yin J, et al. Outcome space range reduction method for global optimization of sum of affine ratios problem. Open Math. 2016;14(1):736–746.
  • Benson H. A simplicial branch and bound duality-bounds algorithm for the linear sum-of-ratios problem. Eur J Oper Res. 2007;182(2):597–611.
  • Benson H. Branch-and-bound outer approximation algorithm for sum-of- ratios fractional programs. J Optim Theory Appl. 2010;146:1–18.
  • Benson H. Using concave envelopes to globally solve the nonlinear sum of ratios problem. J Glob Optim. 2002;22(1/4):343–364.
  • Liu X, Gao Y, Zhang B. A new global optimization algorithm for a class of linear fractional programming. Mathematics. 2019;7(9):867.
  • Jiao H, Wang Z, Chen Y. Global optimization algorithm for sum of generalized polynomial ratios problem. Appl Math Model. 2013;37(1-2):187–197.
  • Wang C, Shen P. A global optimization algorithm for linear fractional programming. Appl Math Comput. 2008;204(1):281–287.
  • Wang C, Shen P. Global optimization for sum of linear ratios problem with coefficients. Appl Math Comput. 2006;176(1):219–229.
  • Shen P, Li W, Liang Y. Branch-reduction-bound algorithm for linear sum-of-ratios fractional programs. Pac J Optim. 2015;11(1):79–99.
  • Wang Y, Zhang K. Global optimization of nonlinear sum of ratios problem. Appl Math Comput. 2004;158(2):319–330.
  • Ji Y, Zhang K, Qu S. A deterministic global optimization algorithm. Appl Math Comput. 2007;185(1):382–387.
  • Costa J. A branch and cut technique to solve a weighted-sum of linear ratios. Pac J Optim. 2010;6(1):21–38.
  • Dur M, Horst R, Thoai N. Solving sum-of-ratios fractional programs using efficient points. Optimization. 2001;49(5-6):447–466.
  • Ashtiani A, Paulo A. A branch-and-cut algorithm for a class of sum-of-ratios problems. Appl Math Comput. 2015;268:596–608.
  • Kuno T. A branch-and-bound algorithm for maximizing the sum of several linear ratios. J Glob Optim. 2002;22(1/4):155–174.
  • Shen PP, Lu T. Regional division and reduction algorithm for minimizing the sum of linear fractional functions. J Inequal Appl. 2018;2018(1):83.
  • Nesterov Y, Nemirovskii A. An interior-point method for generalized linear-fractional programming. Math Program. 2003;69:177–204.
  • Konno H, Abe N. Minimization of the sum of three linear fractional functions. J Glob Optim. 1999;15:419–432.
  • Benson H. On the global optimization of sums of linear fractional func- tions over a convex set. J Optim Theory Appl. 2004;121(1):19–39.
  • Shen P, Huang B, Wang L. Range division and linearization algorithm for a class of linear ratios optimization problems. J Comput Appl Math. 2019;350:324–342.
  • Falk J, Palocsay S. Image space analysis of generalized fractional programs. J Glob Optim. 1994;4(1):63–88.
  • Phuong N, Tuy H. A unified monotonic approach to generalized linear fractional programming. J Glob Optim. 2003;26(3):229–259.
  • Konno H, Yamashita H. Minimizing sums and products of linear fractional functions over a polytope. Nav Res Logist. 1999;46(5):583–596.
  • Benson HP. On the construction of convex and concave envelope formulas for bilinear and fractional functions on quadrilaterals. Comput Optim Appl. 2004;27(1):5–22.
  • Shen P, Wang K, Lu T. Outer space branch and bound algorithm for solving linear multiplicative programming problems. J Glob Optim. 2020;78(3):453–482.
  • Schobel A, Scholz D. The theoretical and empirical rate of convergence for geometric branch-and-bound methods. J Glob Optim. 2010;48(3):473–495.

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