Minimizing the sum of a linear and a linear fractional function applying conic quadratic representation: continuous and discrete problems

References

• Frenk J, Schaible S. Fractional programming, handbook of generalized convexity and generalized monotonicity. In: Hadjisavvas N, Komlosi S, Schaible S, editors. Nonconvex optimization and its applications. Vol. 76. Berlin: Springer; 2005. p. 335–386.
   Google Scholar
• Schaible S. A note on the sum of a linear and linear-fractional function. Naval Res. Logist. Q. 1977;24:691–693.
   Google Scholar
• Konno H, Kuno T, Yajima Y. Global minimization of a generalized convex multiplicative function. J. Global Optim. 1994;4:47–62.
   Web of Science ®Google Scholar
• Benson HP. Concave minimization: theory, applications, and algorithms. In: Horst R, Pardalos PM, editors. Handbook of global optimization. Dordrecht: Kluwer Academic; 1995. p. 43–148.
   Google Scholar
• Benson HP. Deterministic algorithms for constrained concave minimization: a unified critical survey. Naval Res. Logist. 1996;43:765–795.
   Web of Science ®Google Scholar
• Benson HP. On the global optimization of sums of linear fractional functions over a convex set. J. Optim. Theory Appl. 2004;121:19–39.
   Web of Science ®Google Scholar
• Konno H, Fukaishi K. A branch-and-bound algorithm for solving low-rank linear multiplicative and fractional programming problems. J. Global Optim. 2000;18:283–299.
   Web of Science ®Google Scholar
• Kuno T. A branch-and-bound algorithm for maximizing the sum of several linear ratios. J. Global Optim. 2002;22:155–174.
   Web of Science ®Google Scholar
• Jiao H, Guo Y, Shen P. Global optimization of generalized linear fractional programming with nonlinear constraints. Appl. Math. Comput. 2006;183:717–728.
   Web of Science ®Google Scholar
• Gao L, Mishra SK, Shi J. An extension of branch-and-bound algorithm for solving sum-of-nonlinear-ratios problem. Optim. Lett. 2012;6:221–230.
   Web of Science ®Google Scholar
• Sharma KC, Singh J. Quadratic fractional optimization through FGP approach. Int. J. Sci. Res. 2014;3:1342–1346.
   Google Scholar
• Matsui T. NP-hardness of linear multiplicative programming and related problems. J. Global Optim. 1996;9:113–119.
   Web of Science ®Google Scholar
• Benson HP. Fractional programming with convex quadratic forms and functions. Eur. J. Oper. Res. 2006;173:351–369.
   Web of Science ®Google Scholar
• Cai H, Wang Y, Yi T. An approach for minimizing a quadratically constrained fractional quadratic problem with application to the communication over wireless channels. Optim. Methods Softw. 2014;29:310–320.
   Web of Science ®Google Scholar
• Hou X-P, Shen P-P, Wang C-F. Global minimization for generalized polynomial fractional program. Math. Prob. Eng. 2014;2014: 1–12, Article ID 567680.
   Google Scholar
• Cambini A, Martein L, Schaible S. On maximizing a sum of ratios. J. Inform. Optim. Sci. 1989;10:65–79.
   Google Scholar
• Konno H, Yajima Y, Matsui T. Parametric simplex algorithms for solving a special class of nonconvex minimization problems. J. Global Optim. 1991;1:65–81.
   Google Scholar
• Konno H, Yamashita H. Maximizing sums and products of linear fractional functions over a polytope. Naval Res. Logist. 1999;46:583–596.
   Web of Science ®Google Scholar
• Dür M, Horst R, Thoai NV. Solving sum-of-ratios fractional programs using efficient points. Optimization. 2001;49:447–466.
   Web of Science ®Google Scholar
• Carosi L, Martein L. A sequential method for a class of pseudoconcave fractional problems. Cent. Eur. J. Oper. Res. 2008;16:153–164.
   Web of Science ®Google Scholar
• Ben-Tal A, Nemirovski A. Lectures on modern convex optimization: analysis, algorithms, and engineering applications. MPS-SIAM series on optimization. Philadelphia (PA): SIAM; 2001.
   Google Scholar
• Cambini A, Crouzeix J-P, Martin L. On the pseudoconvexity of a quadratic fractional function. Optimization. 2002;51:677–687.
   Web of Science ®Google Scholar
• Charnes A, Cooper WW. Programming with linear fractional functionals. Naval Res. Logist. Q. 1962;9:181–186.
   Google Scholar
• Ahuja RK, Magnanti TL, Orlin JB. Network flows: theory, algorithms, and applications. Englewood cliffs (NJ): Prentice-Hall; 1993.
   Google Scholar
• Hijazi H, Bonami P, Ouorou A. Robust delay-constrained routing in telecommunications. Technical report, CNRS-Aix Marseille Universite; 2012.
   Google Scholar
• Fletcher R, Powell MJD. A rapidly convergent descent method for minimization. Comput. J. 1963;6:163–168.
   Web of Science ®Google Scholar
• Han SP. A globally convergent method for nonlinear programming. J. Optim. Theory Appl. 1977;22:297.
   Web of Science ®Google Scholar
• Powell MJD. A fast algorithm for nonlinearly constrained optimization calculations. In: Watson GA, editor. Numerical analysis. Vol. 630, Lecture notes in mathematics. Berlin: Springer Verlag; 1978.
   Google Scholar
• Powell MJD. The convergence of variable metric methods for nonlinearly constrained optimization calculations. In: Mangasarian OL, Meyer RR, Robinson SM, editors. Nonlinear programming 3. New York (NY): Academic Press; 1978.
   Google Scholar
• Gill PE, Murray W, Wright MH. Practical optimization. London: Academic Press; 1981.
   Google Scholar
• Byrd RH, Hribar ME, Nocedal J. An interior point algorithm for large-scale nonlinear programming. SIAM J. Optim. 1999;9:877–900.
   Web of Science ®Google Scholar
• Byrd RH, Gilbert JC, Nocedal J. A trust region method based on interior point techniques for nonlinear programming. Math. Program. 2000;89:149–185.
   Web of Science ®Google Scholar
• Waltz RA, Morales JL, Nocedal J, et al. An interior algorithm for nonlinear optimization that combines line search and trust region steps. Math. Program. 2006;107:391–408.
   Web of Science ®Google Scholar
• Sharma SC, Bansal A. An integer solution of fractional programming problem. Gen. Math. Notes. 2011;4:1–9.
   Google Scholar
• Li H-L. A global approach for general 0--1 fractional programming. Eur. J. Oper. Res. 1994;73:590–596.
   Web of Science ®Google Scholar
• Wu T-H. A note on a global approach for general 0--1 fractional programming. Eur. J. Oper. Res. 1997;101:220–223.
   Web of Science ®Google Scholar
• Chang C-T. On the polynomial mixed 0–1 fractional programming problems. Eur. J. Oper. Res. 2001;131:224–227.
   Web of Science ®Google Scholar
• Yue D, Guillén-Gosálbez G, You F. Global optimization of large-scale mixed-integer linear fractional programming problems: a reformulation-linearization method and process scheduling applications. Am. Inst. Chem. Eng. J. 2013;59:4255–4272.
   Web of Science ®Google Scholar
• Carosi L, Martein L. On the pseudoconvexity and pseudolinearity of some classes of fractional functions. Optimization. 2007;56:385–398.
   Web of Science ®Google Scholar