Abstract
In this short note we expand the brief discussion in Sniedovich et al [17] concerning the deployment of simplex method in the framework of c-programming as a global optimizer of a large class of DC problems. We use this positive experience to advance the view that, from an algorithmic point of view, DC programming requires further classification and specialisation.
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References
H.P. Benson, and G.M. Boger, Multiplicative Programming Problems: Analysis and an Efficient Point Search Heuristic. To appear in Journal of Optimization Theory and Applications.
J.B. Hirriart-Urruty, Generalized Differentiability, Duality and Optimization for Problems Dealing with Differences of two Convex Functions. Lecture Notes in Economics and Mathematical Systems, 256, Springer-Verlag, Berlin, 1985, 37–69.
P. Hartman, On Functions Representable as a Difference of Convex Functions. Pacific Journal of Mathematics, 9, 707–713, 1959.
R. Horst, A New Branch and Bound Approach for Concave Minimization Problems. Lecture Notes in Computer Science 41, Springer-Verlag, Berlin, 1976, 330–337.
R. Horst, A General Class of Branch and Bound Methods in Global Optimization with some New Approaches for Concave Minimization. Journal of Optimization Theory and Applications, 51, 1986, 271–291.
R. Horst, Recent Advances in Global Optimization: A Tutorial Survey. In Recent Developments in Mathematical Programming, S. Kumar eds., Gordon and Breach Science Publishers, 1991.
R. Horst, and P.M. Pardalos, Handbook of Global Optimization. Kluwer Academic Publishers, Dordrecht, 1995, 369–405.
R. Horst, and H. Tuy, Global Optimization. 2nd Edition, Springer Verlag, Berlin, 1993.
R. Horst, T.Q. Phong, Ng.V. Thoai, and J. de Vries, On Solving a DC programming problem by a sequence of Linear programs. Journal of Global Optimization, 1, 1991, 183–203.
J. Liebman, L. Lasdon, L. Schrage, and A. Waren, Modeling and Optimization with GINO. The Scientific Press, New York, 1986.
H. Konno and T. Kuno, Linear Multiplicative programming. Mathematical programming A 56, 1992, 51–65.
H. Konno and T. Kuno, Multiplicative Programming Problems. In Handbook of Global Optimization, R. Horst and P.M. Pardalos, eds., Kluwer Academic Publishers, Dordrecht, 1995, 369–405.
H. Konno, P.T. Thach and H. Tuy, Optimization on Low Rank Nonconvex Structures. Kluwer Academic Publishers, Dordrecht, 1997.
E. Macalalag and M. Sniedovich, Generalized Linear Programming and Sensitivity Analysis Techniques. Naval Research Logistics, 43, 1996, 397–413.
T.Q. Phong, An algorithm for solving general DC programming problems. Operations Research Letters 15, 1994, 73–79.
M. Sniedovich, Dynamic Programming. Marcel Dekker, New York, 1992.
M. Sniedovich, Algorithmic and Computational Aspects of Composite Concave Programming. International Transactions in Operations Research, 1, No.l, 1994, 75–84.
M. Sniedovich, E. Macalalag and S. Findlay, The Simplex Method as a Global Optimizer: A C-programming perspective. Journal of Global Optimization 4, 1994, 89–109.
M. Sniedovich and S. Findlay, Solving a Class of Multiplicative Programming Problems via C-Programming. Journal of Global Optimization, 6, 1995, 313–319.
H. Tuy, Concave Minimization under Linear Constraints with Special Structure. Optimization, 16, 1985, 335–352.
H. Tuy, Global Minimization of a Difference of Two Convex Functions. Mathematical Programming Study, 30, 1987, 150–182.
N.V. Thoai, A modified version of Tuy’s Method for solving DC programming problems. Optimization, 19, 1988, 665–674.
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© 1999 Kluwer Academic Publishers
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Churilov, L., Sniedovich, M. (1999). A Concave Composite Programming Perspective on DC Programming. In: Progress in Optimization. Applied Optimization, vol 30. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3285-5_12
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DOI: https://doi.org/10.1007/978-1-4613-3285-5_12
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