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H. Benson (2008)
Global Maximization of a Generalized Concave Multiplicative FunctionJournal of Optimization Theory and Applications, 137
C. Maranas, I. Androulakis, C. Floudas, A. Berger, J. Mulvey (1997)
Solving long-term financial planning problems via global optimizationJournal of Economic Dynamics and Control, 21
Kristin Bennett, O. Mangasarian (1993)
Bilinear separation of two sets inn-spaceComputational Optimization and Applications, 2
H. Konno, Yasutoshi Yajima, Tomomi Matsui (1991)
Parametric simplex algorithms for solving a special class of nonconvex minimization problemsJournal of Global Optimization, 1
T. Kuno, Yasutoshi Yajima, H. Konno (1993)
An outer approximation method for minimizing the product of several convex functions on a convex setJournal of Global Optimization, 3
N. Thoai (1991)
A global optimization approach for solving the convex multiplicative programming problemJournal of Global Optimization, 1
R. Cambini, C. Sodini (2005)
Decomposition Methods for Solving Nonconvex Quadratic Programs via Branch and Bound*Journal of Global Optimization, 33
J. Falk, Susan Palocsay (1994)
Image space analysis of generalized fractional programsJournal of Global Optimization, 4
Xue-gang Zhou, Kun Wu (2009)
A method of acceleration for a class of multiplicative programming problems with exponentJournal of Computational and Applied Mathematics, 223
Kristin Bennett (2007)
Global Tree Optimization: A Non-greedy Decision Tree Algorithm
H. Konno, T. Kuno, Yasutoshi Yajima (1994)
Global minimization of a generalized convex multiplicative functionJournal of Global Optimization, 4
P. Shen, Hongwei Jiao (2006)
Linearization method for a class of multiplicative programming with exponentAppl. Math. Comput., 183
T. Kuno (1999)
Solving a Class of Multiplicative Programs with 0–1 Knapsack ConstraintsJournal of Optimization Theory and Applications, 103
H. Benson, G. Boger (2000)
Outcome-Space Cutting-Plane Algorithm for Linear Multiplicative ProgrammingJournal of Optimization Theory and Applications, 104
X. Liu, T. Umegaki, Y. Yamamoto (1999)
Heuristic Methods for Linear Multiplicative ProgrammingJournal of Global Optimization, 15
(1995)
Global optimization algorithms for chip design and compaction. Engineering Optimization
M.C. Dorneich, N.V. Sahinidis (1995)
Global optimization algorithms for chip design and compactionEngineering Optimization, 25
Tomomi Matsui (1996)
NP-hardness of linear multiplicative programming and related problemsJournal of Global Optimization, 9
H. Ryoo, N. Sahinidis (2003)
Global Optimization of Multiplicative ProgramsJournal of Global Optimization, 26
H. Benson (1999)
An Outcome Space Branch and Bound-Outer Approximation Algorithm for Convex Multiplicative ProgrammingJournal of Global Optimization, 15
S. Strauss (2016)
Convex Analysis And Global Optimization
J. Mulvey, R. Vanderbei, S. Zenios (1995)
Robust Optimization of Large-Scale SystemsOper. Res., 43
H. Konno, T. Kuno (1991)
Generalized linear multiplicative and fractional programmingAnnals of Operations Research, 25
S. Schaible, C. Sodini (1995)
Finite algorithm for generalized linear multiplicative programmingJournal of Optimization Theory and Applications, 87
I. Quesada, I.E. Grossmann (1996)
Global Optimization in Engineering Design, Nonconvex Optimization and Its Applications
H. Benson, G. Boger (1997)
Multiplicative Programming Problems: Analysis and Efficient Point Search HeuristicJournal of Optimization Theory and Applications, 94
R. Horst, T. Hoang (1992)
Global Optimization: Deterministic Approaches
I. Quesada, I. Grossmann (1996)
Alternative Bounding Approximations for the Global Optimization of Various Engineering Design Problems
P.M. Pardalos (1990)
Polynomial time algorithms for some classes of constrained quadratic problemsOptimization, 21
In this paper, a new global algorithm is presented to globally solve the linear multiplicative programming (LMP). The problem (LMP) is firstly converted into an equivalent programming problem (LMP (H)) by introducing p auxiliary variables. Then by exploiting structure of (LMP(H)), a linear relaxation programming (LP (H)) of (LMP (H)) is obtained with a problem (LMP) reduced to a sequence of linear programming problems. The algorithm is used to compute the lower bounds called the branch and bound search by solving linear relaxation programming problems (LP(H)). The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jun 19, 2015
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