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Thi Bach Kim NGUYEN(kimntbfamimail.hut.edu.vn) Abstract: This paper presents an outcomespace outer approximation algorithm for solving the problem of minimizing the product of two convex functions over a compact convex set in $\R^n$. The computational experiences are reported. The proposed algorithm is convergent. Keywords: global optimization problem, efficient point, outcome set, minimizing the product of two convex functions Category 1: Global Optimization Category 2: Nonlinear Optimization Citation: [1] H. P. Benson and G. M. Boger, Multiplicative Programming Problems: Analysis and Efficient Point Search Heuristic, Journal of Optimization Theory and Applications, 94, pp. 487510, 1997. [2] H. P. Benson and G. M. Boger, OutcomeSpace CuttingPlane Algorithm for Linear Multiplicative Programming, Journal of Optimization Theory and Applications, 104, pp. 301322, 2000. [3] H. P. Benson, An Outcome Space Branch and BoundOuter Approximation Algorithm for Convex Multiplicative Programming, Journal of Global Optimization, 15, pp. 315 342, 1999. [4] Y. Gao, G. Wu and W. Ma, A New Global Optimization Approach for Convex Multi plicative Programming, Applied Mathematics and Computation, 216, pp. 12061218, 2010. [5] R. Hosrt, N. V. Thoai and J. Devries, On Finding the New Vertices and Redundant Constraints in Cutting Plane Algorithms for Global Optimization, Operations Research Letters 7, pp. 8590, 1988. [6] N. T. B. Kim, Finite Algorithm for Minimizing the Product of Two Linear Functions over a Polyhedron, Journal Industrial and Management Optimization, 3(3), pp. 481 487, 2007. [7] N. T. B. Kim, N. T. L. Trang and T. T. H. Yen, OutcomeSpace Outer Approximation Algorithm for Linear Multiplicative Programming, East West Journal of Mathematics, 9(1), pp. 8198, 2007. [8] H. Konno and T. Kuno, Linear Multiplicative Programming, Mathematical Program ming, 56, pp. 5164, 1992. [9] H. Konno and T. Kuno, Multiplicative Programming Problems, Handbook of Global Optimization, Edited by R. Horst and P.M. Pardalos, Kluwer Academic Publishers, Dordrecht, Netherlands, pp. 369405, 1995. [10] D. T. Luc, “Theory of Vector Optimization”, SpringerVerlag, Berlin, Germany, 1989. [11] T. Matsui, NPHardness of Linear Multiplicative Programming and Related Problems, Journal of Global Optimization, 9, pp. 113119, 1996. [12] L. D. Muu and B. T. Tam, Minimizing the Sum of a Convex Function and the Product of Two Affine Functions over a Convex set, Optimization, 24, pp. 5762, 1992. [13] H. X. Phu, On Efficient Sets in R2, Vietnam Journal of Mathematics, 33(4), pp. 463468, 2005. [14] R. T. Rockafellar, “Convex Analysis”, Princeton University Press, Princeton, 1970. [15] T. V. Thieu, A Finite Method for Globally Minimizing Concave Function over Un bounded Polyhedral Convex Sets and Its Applications, Acta Mathematica Hungarica 52, 2136, 1988. [16] N. V. Thoai, A Global Optimization Approach for Solving the Convex Multiplicative Programming Problem, Journal of Global Optimization, 1, pp. 341357, 1991. [17] P. L. Yu, “MultipleCriteria Decision Making”, Plenum Press, New York and London, 1985. Download: [PDF] Entry Submitted: 06/24/2011 Modify/Update this entry  
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