Abstract
In this paper we give a brief account of the important role that the conventional simplex method of linear programming can play in global optimization, focusing on its collaboration with composite concave programming techniques. In particular, we demonstrate how rich and powerful the c-programming format is in cases where its parametric problem is a standard linear programming problem.
Similar content being viewed by others
References
Avriel, M. (1976),Nonlinear Programming: Analysis and Methods, Prentice-Hall, Englewood Cliffs, New Jersey.
Bazaraa, M. S., J. J. Jarvis, and H. D. Sherali (1990),Linear Programming and Network Flows, Wiley, New York.
Bazaraa, M. S. and C. M. Shetty (1979),Nonlinear Programming, Theory and Algorithms, John Wiley, New Jersey.
Craven, B. D. (1988),Fractional Programming, Heldermann Verlag, Berlin.
Frank, M. and Wolfe, P. (1956), An Algorithm for Quadratic Programming,Naval Research Logistics Quarterly 3, 95–110.
Hillier, F. S. and G. J. Lieberman (1990),Introduction to Operations Research (5th ed., McGraw-Hill, New York.
Horst, R. T. Q. Phong, Ng. V Thoai, and J. Vries (1991), On Solving a d.c. Programming Problem by a Sequence of Linear Programs,Journal of Global Optimization 1, 183–203.
Horst, R. and H. Tuy (1990),Global Optimization: Deterministic Approaches, Springer-Verlag, Berlin.
Katoh, N. and T. Ibaraki (1987), A Parametric Characterization of an ɛ-Approximation Scheme for the Minimization of a Quasiconcave Program,Discrete Applied Mathematics 17, 39–66.
Konno, H. and T. Kuno (1992), Linear Multiplicative Programming,Mathematical Programming A 56, 51–65.
Konno, H., Y. Yajima, and T. Matsui (1991), Parametric Simplex Algorithms for Solving a Special Class of Nonconvex Minimization Problems,Journal of Global Optimization 1, 65–81.
Kuno, T. and H. Konno (1991), A Parametric Successive Underestimation Method for Convex Multiplicative Programming Problems,Journal of Global Optimization 1, 267–285.
Liebman J., L. Lasdon, L. Schrage, and A. Warren (1986),Modelling and Optimization with GINO, The Scientific Press, San Francisco.
Macalalag, E. and M. Sniedovich (1991), On the Importance of Being a Sensitive lp Package, Preprint Series No. 3-1991, Department of Mathematics, The University of Melbourne.
Schaible, S. (1976), Fractional Programming.1, Duality,Management Science 22, 858–867.
Schrage, L., (1991),LINDO: An Optimization Modelling System (ed., The Scientific Press, San Francisco.
Sniedovich, M. (1985), C-Programming: An Outline,Operations Research Letters 1(1), 19–21.
Sniedovich, M. (1986), C-Programming and the Minimization of Pseudolinear and Additive Concave Functions,Operations Research Letters 5(4), 185–189.
Sniedovich, M. (1989), Analysis of a Class of Fractional Programming Problems,Mathematical Programming 43(3), A, 329–347.
Sniedovich, M. (1992),Dynamic Programming, Marcel Dekker, New York.
Yajima, Y. and H. Konno (1991), Efficient Algorithms for Solving Rank Two and Rank Three Bilinear Programming Problems,Journal of Global Optimization 1, 155–171.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sniedovich, M., Macalalag, E. & Findlay, S. The simplex method as a global optimizer: A c-programming perspective. J Glob Optim 4, 89–109 (1994). https://doi.org/10.1007/BF01096536
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01096536