A hybrid method for solving non-convex min–max quadratic fractional problems under quadratic constraints

References

• Schaible S, Ziemba W. T. Generalized concavity in optimization and economics. New York: Academic Press; 1981. Chapter V, A survey of fractional programming; p. 417–440.
   Google Scholar
• Crouzeix JP, Ferland JA. Algorithms for generalized fractional programming. Math Program. 1991;52(1):191–207.
   Web of Science ®Google Scholar
• Von Neumann J. A model of general economic equilibrium. Rev Econom Stud. 1945;13:1–9.
   Web of Science ®Google Scholar
• Barrodale I, Powell MJD, Roberts FDK. The differential correction algorithm for rational l∞ approximation. SIAM J Numer Anal. 1972;9:493–504.
   Web of Science ®Google Scholar
• Crouzeix JP, Ferland JA, Schaible S. Duality in generalized linear fractional programming. Math Program. 1983;27:342–354.
   Web of Science ®Google Scholar
• Jagannathan R. An algorithm for a class of nonconvex programming problems with nonlinear fractional objectives. Manage Sci. 1985;31:847–851.
   Web of Science ®Google Scholar
• Schaible S. Multiratio fractional programming – a survey. In Kurzhanski A, Neumann K and Pallaschke D, editors. Optimization, parallel processing and applications. Lect. Notes Econ. Math. Syst; 1988; Vol. 304. p. 57–66.
   Google Scholar
• Crouzeix JP, Ferland JA, Schaible S. An algorithm for generalized fractional programs. J Optim Theory Appl. 1985;47:35–49.
   Web of Science ®Google Scholar
• Benadada Y, Fedand JA. Partial linearization for generalized fractional programming. Z Oper Res. 1988;32:101–106.
   Google Scholar
• Freund RW, Jarre F. An interior-point method for fractional programs with convex constraints. Math Program. 1994;67:407–440.
   Web of Science ®Google Scholar
• Barros AI, Frenk JBG. Generalized fractional programming and cutting plane algorithms. J Optim Theory Appl. 1995;87:103–120.
   Web of Science ®Google Scholar
• Feng Q, Jiao H, Mao H, et al. A deterministic algorithm for min-max and max-min linear fractional programming problems. Int J Comput Intell Syst. 2011;4:134–141.
   Web of Science ®Google Scholar
• Feng Q, Mao H, Jiao H. A feasible method for a class of mathematical problems in manufacturing system. Key Eng Mater. 2011;460–461:806–809.
   Google Scholar
• Borde J, Crouzeix JP. Convergence of a Dinkelbach-type algorithm in generalized fractional programming. Z Oper Res. 1987;31(1):A31–A54.
   Google Scholar
• Jiao H, Liu S. A new linearization technique for minimax linear fractional programming. Int J Comput Math. 2014;91(8):1730–1743.
   Web of Science ®Google Scholar
• Zhao Y, Liu S, Jiao H. A new branch and bound algorithm for minimax ratios problems. Open Math. 2017;15:840–851.
   Web of Science ®Google Scholar
• Amaral PA, Bomze IM. Nonconvex min–max fractional quadratic problems under quadratic constraints: copositive relaxations. J Global Optim. 2019;75:227–245.
   Web of Science ®Google Scholar
• Dinkelbach W. On nonlinear fractional programming. Manage Sci. 1967;13:492–498.
   Google Scholar
• Garey MR, Johnson DS. Computers and intractability: a guide to the theory of NP-completeness. San Francisco: W.H. Freeman and co.; 1979.
   Google Scholar
• Yuille AL, Rangarajan A. The concave-convex procedure. Neural Comput. 2003;15:915–936.
   PubMed Web of Science ®Google Scholar
• Sriperumbudur BK, Lanckriet G. A proof of convergence of the concave-convex procedure using zangwill's theory. Neural Comput. 2012;24(6):1391–1407.
   PubMed Web of Science ®Google Scholar
• Lipp T, Boyd S. Variations and extension of the convex–concave procedure. Optim Engin. 2016;17:263–287.
   Web of Science ®Google Scholar
• Crouzeix JP, Ferland JA, Schaible S. A note on an algorithm for generalized fractional programs. J Optim Theory Appl. 1986;50:183–187.
   Web of Science ®Google Scholar
• Boyd S, Vandenberghe L. Convex optimization. Cambridge: Cambridge University Press; 2009.
   Google Scholar
• Ben-Tal A, Nemirovski A. Lectures on modern convex optimization: analysis, algorithms, and engineering applications. Philadelphia: SIAM; 2001.
   Google Scholar
• Santana A, Dey SS. The convex hull of a quadratic constraint over a polytope. SIAM J Optim. 2018;30(4):2983–2997.
   Web of Science ®Google Scholar
• Deng Zh, Fang Sh, Jin Q, et al. Conic approximation to nonconvex quadratic programming with convex quadratic constraints. J Glob Optim. 2015;61:459–478.
   Web of Science ®Google Scholar
• Keyanpour M, Osmanpour N. On solving quadratically constrained quadratic programming problem with one non-convex constraint. Opsearch. 2018;55(2):320–336.
   Web of Science ®Google Scholar
• Grant M, Boyd S. CVX: Matlab software for disciplined convex programming, version 1.21. 2011; Available from: http://cvxr.com/cvx/.
   Google Scholar
• Zhang XJ, Sun XL, Li D. Nonconvex quadratically constrained quadratic programming: best D.C.decomposition and their SDP representations. J Glob Optim. 2011;50:695–712.
   Web of Science ®Google Scholar
• Dolan E, More JJ. Benchmarking optimization software with performance profiles. Math Program. 2002;91:201–213.
   Web of Science ®Google Scholar