Global optimization algorithm for solving linear multiplicative programming problems

References

• Maranas CD, Androulakis IP, Flounda CA, et al. Solving long-term financial planning problems via global optimization. J Econ Dyn Control. 1997;21:1405–1425.
   Web of Science ®Google Scholar
• Kahl F, Agarwal S, Chandraker MK, et al. Practical global optimization for multiview geometry. Int J Comput Vis. 2008;79(3):271–284.
   Web of Science ®Google Scholar
• Quesada I, Grossmann IE. Alternative bounding approximations for the global optimization of various engineering design problems. In: Grossmann IE editor. Global optimization in engineering design, nonconvex optimization and its applications, Vol. 9. Norwell (MA): Kluwer Academic; 1996.
   Google Scholar
• Bennett KP, Mangasarian OL. Bilinear separation of two sets in n-space. Comput Optim Appl. 1994;2:207–227.
   Google Scholar
• Dorneich MC, Sahinidis NV. Global optimization algorithms for chip design and compaction. Eng Optim. 1995;25(2):131–154.
   Web of Science ®Google Scholar
• Mulvey JM, Vanderbei RJ, Zenios SA. Robust optimization of large-scale systems. Oper Res. 1995;43:264–281.
   Web of Science ®Google Scholar
• Konno H. Globally determining a minimum-aera hyperrectangle enclosing the projection of a bigger dimensional set. Oper Res Lett. 1993;13:295–303.
   Web of Science ®Google Scholar
• Konno H, Wantanabe H. Bond portfolio optimization problems and their applications to index tracking. J Oper Res Soc Japan. 1994;39(3):295–306.
   Google Scholar
• Shen PP, Yang LP, Liang YC. Range division and contraction algorithm for a class of global optimization problems. Appl Math Comput. 2014;242:116–126.
   Web of Science ®Google Scholar
• Cambini A, Martein L. Generalized convexity and optimization: theory and applications. Lecture notes in economics and mathematical systems. Berlin: Springer; 2009.
   Google Scholar
• Cambini R, Sodini C. On the minimization of a class of generalized linear functions on a flow polytope. Optimization. 2014;63(10):1449–1464.
   Web of Science ®Google Scholar
• Tuy H. Convex analysis and global optimization. Dordrecht: Kluwer Academic; 1998.
   Google Scholar
• Konno H, Yajima Y. Solving rank two bilinear programs by parametric simplex algorithms. Institute of Human and Social Sciences Working Paper IHSS 90-17. Tokyo, Japan: Tokyo Institute of Technology; 1990.
   Google Scholar
• Raghavachari M. On connections between zero-one integer programming and concave programming under linear constraints. Oper Res. 1969;17:680–684.
   Web of Science ®Google Scholar
• Floudas CA, Visweswaran V. Quadratic optimization. Boston: Springer; 1995.
   Google Scholar
• Horst R, Pardalos PM, Thoai NV. Introduction to global optimization. Dordrecht: Kluwer Academic Publishers; 1995.
   Google Scholar
• Konno H, Thach PT, Tuy H. Optimization on low rank nonconvex structures. Dordrecht: Kluwer Academic; 1997.
   Google Scholar
• Matsui T. NP-hardness of linear multiplicative programming and related problem. J Global Optim. 1996;9:113–119.
   Web of Science ®Google Scholar
• Gao YL, Wu GR, Ma WM. A new global optimization approach for convex multiplicative programming. Appl Math Comput. 2010;216:1206–1218.
   Web of Science ®Google Scholar
• Zhou XG, Wu K. A method of acceleration for a class of multiplicative programming with exponent. J Comput Appl Math. 2009;223:975–982.
   Web of Science ®Google Scholar
• Jiao HW, Liu SY, Chen YQ. Global optimization algorithm of a generalized linear multiplicative programming. J Appl Math Comput. 2012;40:551–568.
   Google Scholar
• Yang LP, Shen PP, Pei YG. A global optimization approach for solving generalized nonlinear multiplicative programming problem. Abstr Appl Anal. 2014; doi: https://doi.org/10.1155/2014/641909
   Google Scholar
• Wang CF, Bai YQ, Shen PP. A practicable branch-and-bound algorithm for globally solving multiplicative programming. Optimization. 2017;66(3):397–405.
   Web of Science ®Google Scholar
• Shen PP, Huang BD. Global algorithm for solving linear multiplicative programming problems. Optim Lett. 2020;14:693–710.
   Web of Science ®Google Scholar
• Zhao YF, Zhao T. Global optimization for generalized linear multiplicative programming using convex relaxation. Math Probl Eng. 2018. doi: https://doi.org/10.1155/2018/9146309
   Web of Science ®Google Scholar
• Zhao YF, Liu SY. An efficient method for generalized linear multiplicative programming problem with multiplicative constraints. SpringerPlus. 2016. doi: https://doi.org/10.1186/s40064-016-2984-9
   Google Scholar
• Gao YL, Xu CX, Yang YT. Outcome-space branch and bound algorithm for solving linear multiplicative programming. Comput Intell Secy. 2005;3801:675–681.
   Web of Science ®Google Scholar
• Wang CF, Liu SY, Shen PP. Global minimization of a generalized linear multiplicative programming. Appl Math Model. 2012;36:2446–2451.
   Web of Science ®Google Scholar
• Konno H, Kuno T, Yajima Y. Global minimization of a generalized convex multiplicative function. J Global Optim. 1994;4(1):47–62.
   Web of Science ®Google Scholar
• Benson HP. Global maximization of a generalized concave multiplicative function. J Optim Theory Appl. 2008;137:150–120.
   Web of Science ®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
• Schaible S, Sodini C. Finite algorithm for generalized multiplicative programming. J Optim Theory Appl. 1995;87(2):441–455.
   Web of Science ®Google Scholar
• Luo HZ, Bai XD, Lim G, et al. New global algorithms for quadratic programming with a few negative eigenvalues based on alternative direction method and convex relaxation. Math Program Comput. 2019;11:119–171.
   Web of Science ®Google Scholar
• Luo HZ, Bai XD, Lim G, et al. Enhancing semidefinite relaxation for quadratically constrained quadratic programming via penalty methods. J Optim Theory Appl. 2019;180:964–992.
   Web of Science ®Google Scholar
• Shen PP, Gu MN. Aduality-bounds algorithm for non-convex quadratic programs with additional multiplicative constraints. Appl Math Comput. 2008;198(1):1–11.
   Web of Science ®Google Scholar
• Kuno T, Yajima Y, Konno H. An outer approximation method for minimizing the product of several convex functions on a convex set. J Global Optim. 1993;3(3):325–335.
   Web of Science ®Google Scholar
• Benson HP, Boger GM. Outcome-space cutting-plane algorithm for linear multiplicative programming. J Optim Theory Appl. 2000;104:301–332.
   Web of Science ®Google Scholar
• Liu XJ, Umegaki T, Yamamoto Y. Heuristic methods for linear multiplicative program-ming. J Global Optim. 1999;4:433–447.
   Web of Science ®Google Scholar
• Shen PP, Wang CF. Linear decomposition approach for a class of nonconvex programming problems. J Inequal Appl. 2017; 2017: 74. doi: https://doi.org/10.1186/s13660-017-1342-y
   PubMed Web of Science ®Google Scholar
• Bennett KP. Global tree optimization: a non-greedy decision tree algorithm. Comput Sci Stat. 1994;26:156–160.
   Google Scholar
• Tuy H, Nghia ND. Reverse polyblock approximation for generalized multiplicative / fractional programming. Vietnam J Math. 2003;31(4):391–402.
   Google Scholar
• Shen PP, Zhang TL, Wang CF. Solving a class of generalized fractional programming problems using the feasibility of linear programs. J Inequal Appl. 2017;2017:147. doi: https://doi.org/10.1186/s13660-017-1420-1
   PubMed Web of Science ®Google Scholar
• Oliveira RM, Ferreira AVP. An outcome space approach for generalized convex multiplicative programs. J Global Optim. 2010;47:107–118.
   Web of Science ®Google Scholar
• Chen Y, Jiao H. A nonisolated optimal solution of general linear multiplicative programming problems. Comput Oper Res. 2009;36:2573–2579.
   Web of Science ®Google Scholar
• Liu SY, Zhao YF. An efficient algorithm for globally solving generalized linear multiplicative programming. J Comput Appl Math. 2016;296:840–847.
   Web of Science ®Google Scholar
• Cambini R, Sodini C. A unifying approach to solve some classes of rank-three multiplicative and fractional programs involving linear functions. Eur J Oper Res. 2010;207:25–29.
   Web of Science ®Google Scholar
• Cambini R, Sodini C. Global optimization of a rank-two nonconvex program. Math Methods Oper Res. 2010;71(1):165–180.
   Web of Science ®Google Scholar
• Goyal V, Genc-Kaya L, Ravi R, An FPTAS for minimizing the product of two non-negative linear cost functions. Math Program. 2011;126:401–405.
   Web of Science ®Google Scholar
• Sahinidis NV, BARON: a general purpose global optimization software package. J Global Optim. 1996;8:201–205.
   Web of Science ®Google Scholar