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A method of acceleration for a class of multiplicative programming problems with exponent. (English) Zbl 1159.65067

Authors’ summary: Multiplicative programming problems with exponent (MPE) have many practical applications in various fields. In this paper, a method for accelerating global optimization is proposed for a class of multiplicative programming problems with exponent under multiplicative constraints using a suitable deleting technique. This technique offers the possibility of cutting away a large part of the currently investigated region in which the globally optimal solution of the MPE does not exist. The deleting technique can accelerate the convergence of the proposed global optimization algorithm. Two numerical examples are given to illustrate the feasibility of the deleting technique.

MSC:

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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[1] Maranas, C.D.; Androulakis, I.P.; Floudas, C.A.; Berger, A.J.; Mulvey, J.M., Solving long-term financial planning problems via global optimization, Journal of economic dynamics and control, 21, 1405-1425, (1997) · Zbl 0901.90016
[2] Quesada, I.; Grossmann, I.E., Alternative bounding approximations for the global optimization of various engineering design problems, (), 309-331 · Zbl 0879.90189
[3] Mulvey, J.M.; Vanderbei, R.J.; Zenios, S.A., Robust optimization of large-scale systems, Operations research, 43, 264-281, (1995) · Zbl 0832.90084
[4] Kuno, T.; Yajima, Y.; Konno, H., An outer approximation method for minimizing the product of several convex functions on a convex set, Journal of global optimization, 3, 3, 325-335, (1993) · Zbl 0798.90117
[5] Benson, H.P., Decomposition branch and bound based algorithm for linear programs with additional multiplicative constraints, Journal of optimization theory and applications, 126, 1, 41-46, (2005) · Zbl 1093.90040
[6] Kuno, T., A finite branch and bound algorithm for linear multiplicative programming, Computational optimization and application, 20, 119-135, (2001) · Zbl 0983.90075
[7] Ryoo, H.S.; Sahinidis, N.V., Global optimization of multiplicative programs, Journal of global optimization, 26, 387-418, (2003) · Zbl 1052.90091
[8] Schaible, S.; Sodini, C., Finite algorithm for generalized linear multiplicative programming, Journal of optimization theory and applications, 87, 2, 441-455, (1995) · Zbl 0839.90113
[9] Benson, H.P.; Boger, G.M., Outcome-space cutting-plane algorithm for linear multiplicative programming, Journal of optimization theory and applications, 104, 2, 301-322, (2000) · Zbl 0962.90024
[10] Liu, X.J.; Umegaki, T.; Yamamoto, Y., Heuristic methods for linear multiplicative programming, Journal of global optimization, 4, 15, 433-447, (1999) · Zbl 0966.90051
[11] Shen, Peiping; Jiao, Hongwei, Linearization method for a class of multiplicative programming with exponent, Applied mathematics and computation, 183, 328-336, (2006) · Zbl 1110.65051
[12] Maranas, C.D.; Floudas, C.A., Global optimization in generalized geometric programming, Computers and chemical engineering, 21, 4, 351-C369, (1997)
[13] Horst, R.; Tuy, H., Global optimization, deterministic approaches, (1990), Springer-Verlag Berlin · Zbl 0704.90057
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