zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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 {\it 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:
90C26Nonconvex programming, global optimization
WorldCat.org
Full Text: DOI
References:
[1] Jiao, H.: A branch and bound algorithm for globally solving a class of nonconvex programming problems. Nonlinear anal. 70, No. 2, 1113-1123 (2008) · Zbl 1155.90459
[2] Henderson, J. M.; Quandt, R. E.: Microeconomic theory. (1971) · 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)
[5] Quesada, I.; Grossmann, I. E.: Alternative bounding approximations for the global optimization of various engineering design problems. Nonconvex optimization and its applications 9, 309-331 (1996) · 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, No. 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, No. 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, No. 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, No. 4, 351-369 (1997)
[18] Shen, P. P.; Jiao, H. W.: Linearization method for a class of multiplicative programming with exponent. Appl. math. Comput. 183, No. 1, 328-336 (2006) · Zbl 1110.65051
[19] Tuy, H.: Convex analysis and global optimization. (1998) · Zbl 0904.90156
[20] Horst, R.; Tuy, H.: Global optimization: deterministic approaches. (1993) · Zbl 0704.90057