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A new accelerating method for globally solving a class of nonconvex programming problems. (English) Zbl 1168.90576

Summary: We combine the new global optimization method proposed by H. Jiao [Nonlinear Anal., Theory Methods Appl. 70, No. 2 (A), 1113–1123 (2009; Zbl 1155.90459)] with a suitable deleting technique to propose a new accelerating global optimization algorithm for solving a class of nonconvex programming problems (NP). This technique offers a possibility to cut away a large part of the currently investigated region in which the global optimal solution of NP does not exist, and can be seen as an accelerating device for the global optimization algorithm of the nonconvex programming problems. Compared with the method in the above cited reference, numerical results show that the computational efficiency is obviously improved by using this new technique in the number of iterations, the required list length and the overall execution time of the algorithm.

MSC:

90C26 Nonconvex programming, global optimization

Citations:

Zbl 1155.90459
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References:

[1] Jiao, H., A branch and bound algorithm for globally solving a class of nonconvex programming problems, Nonlinear anal., 70, 2, 1113-1123, (2008) · Zbl 1155.90459
[2] Henderson, J.M.; Quandt, R.E., Microeconomic theory, (1971), McGraw-Hill New York · Zbl 0224.90014
[3] Maranas, C.D.; Androulakis, I.P.; Floudas, C.A.; Berger, A.J.; Mulvey, J.M., Solving long-term financial planning problems via global optimization, J. econom. dynam. control, 21, 1405-1425, (1997) · Zbl 0901.90016
[4] Markowitz, H.M., Portfolio selection, (1991), Basil Blackwell Inc. Oxford
[5] Quesada, I.; Grossmann, I.E., Alternative bounding approximations for the global optimization of various engineering design problems, (), 309-331 · Zbl 0879.90189
[6] Mulvey, J.M.; Vanderbei, R.J.; Zenios, S.A., Robust optimization of large-scale systems, Oper. res., 43, 264-281, (1995) · Zbl 0832.90084
[7] Hoai-Phuony, Ng.T.; Tuy, H., A unified monotonic approach to generalized linear fractional programming, J. global optim., 26, 229-259, (2003) · Zbl 1039.90079
[8] Benson, H.P., A simplicial branch and bound duality-bounds algorithm for the linear sum-of-ratios problem, European J. oper. res., 182, 597-611, (2007) · Zbl 1121.90102
[9] Wang, Y.J.; Shen, P.P.; Liang, Z.A., A branch-and-bound algorithm to globally solve the sum of several linear ratios, Appl. math. comput., 168, 89-101, (2005) · Zbl 1079.65071
[10] Jiao, H.W.; Guo, Y.R.; Shen, P.P., Global optimization of generalized linear fractional programming with nonlinear constraints, Appl. math. comput., 183, 2, 717-728, (2006) · Zbl 1111.65052
[11] Gao, Y.L.; Xu, C.X.; Yan, Y.L., An outcome-space finite algorithm for solving linear multiplicative programming, Appl. math. comput., 179, 2, 494-505, (2006) · Zbl 1103.65065
[12] Benson, H.P., Decomposition branch and bound based algorithm for linear programs with additional multiplicative constraints, J. optim. theory appl., 126, 41-46, (2005) · Zbl 1093.90040
[13] Ryoo, H.S.; Vsahinidis, N., Global optimization of multiplicative programs, J. global optim., 26, 387-418, (2003) · Zbl 1052.90091
[14] Schaible, S.; Sodini, C., Finite algorithm for generalized linear multiplicative programming, J. optim. theory appl., 87, 2, 441-455, (1995) · Zbl 0839.90113
[15] Shen, P.P.; Jiao, H.W., A new rectangle branch-and-pruning approach for generalized geometric programming, Appl. math. comput., 183, 1027-1038, (2006) · Zbl 1112.65058
[16] Wang, Y.J.; Liang, Z.A., A deterministic global optimization algorithm for generalized geometric programming, Appl. math. comput., 168, 722-737, (2005) · Zbl 1105.65335
[17] Maranas, C.D.; Floudas, C.A., Global optimization in generalized geometric programming, Comput. chem. eng., 21, 4, 351-369, (1997) · Zbl 0891.90165
[18] Shen, P.P.; Jiao, H.W., Linearization method for a class of multiplicative programming with exponent, Appl. math. comput., 183, 1, 328-336, (2006) · Zbl 1110.65051
[19] Tuy, H., Convex analysis and global optimization, (1998), Kluwer Academic Dordrecht · Zbl 0904.90156
[20] Horst, R.; Tuy, H., Global optimization: deterministic approaches, (1993), Springer Berlin, Germany
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