Abstract
The problem to be addressed in this paper is that of finding the global minimum of a difference of two given convex functions: \({x_{n_2 } \in R^{n_1 } ,}\), over a given polyhedral convex set in \(R^{n_1 } x\,R^{n_2 } \).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. Balas. Nonconvex quadratic programming via generalized polars. SIAM J. Appl. Math. 28 (1975), 335–349.
A.V. Cabot, R.L. Francis. Solving certain nonconvex quadratic minimization problems by ranking extreme points. Opns. Res. 18 (1970), 82–86.
J.E. Falk, R.M. Soland. An algorithm for separable nonconvex programming problems. Management Science 15 (1969), 550–569.
A. Geoffrion. Generalized Benders decompositions. J. Optim. Theory Appl. 10 (1972), 237–260.
L.A. Istomin. A modification of H. Tuy’s method for minimizing a concave function over a polytope. Ž. Vyčisl. Mat, i. Mat. Fiz. 17 (1977), 1592–1597 (Russian).
H. Konno. Maximization of a convex quadratic function under linear constraints. Math. Programming 11 (1976), 117–127.
Paul F. Kough. The indefinite quadratic programming problem. Opns. Res. 27 (1979), 516–533.
P.A. Meyer. Probabilités et potentiels. Herman. Paris 1966.
B.M. Mukhamediev. Approximate method for solving concave programming problems. Ž. Vyčisl. Mat. i Mat. Fiz. 22 (1982), 727–732 (Russian).
K. Ritter. A method for solving maximum problems with a nonconcave quadratic objective function. Z. Wahrscheinlichkeitstheor. Verw. Geb. 4 (1966), 340–351.
R.T. Rockafellar. Convex analysis. Princeton University Press 1970.
J.B. Rosen. Global minimization of a linearly constrained concave function by partition of feasible domain. Math. Oper. Res. (to appear).
J.B. Rosen. Parametric global minimization for large scale problems. Math. Oper. Res. (to appear).
K. Tammer. Möglichkeiten zur Anwendung der Erkenntnis der parametrischen Optimierung für die Lösung indefiniter quadratischer Optimierungsprobleme. Math. Operationsforsch. u. Statist. 7 (1976), 209–222.
Ng. v. Thoai, H. Tuy. Convergent algorithms for minimizing a concave function. Math. Oper. Res. 5 (1980), 556–566.
H. Tuy. Concave programming under linear constraints. Doklady Akad. Nauk 159 (1964), 32–35. Translated Soviet Math. 5 (1964), 1437-1440.
H. Tuy. The Farkas-Minkowski theorem and extremum problems. In the book “Mathematical Models in Economics”, J. Loś and M.W. Loś eds. Warszawa 1974, 379-400.
H. Tuy. Global maximization of a convex function over a closed, convex, not necessarily bounded set. Cahiers de Mathématiques de la Décision. No. 8223 CEREMADE. Université Paris-Dauphine. 1982.
H. Tuy. Improved algorithm for solving a class of global minimization problems. Preprint. Institute of Mathematics, Hanoi 1983.
H. Tuy. On outer approximation methods for solving concave minimization problems. Submitled to Acta Math. Vietnamica 1983.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tuy, H. (1984). Global Minimization of a Difference of Two Convex Functions. In: Hammer, G., Pallaschke, D. (eds) Selected Topics in Operations Research and Mathematical Economics. Lecture Notes in Economics and Mathematical Systems, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45567-4_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-45567-4_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12918-9
Online ISBN: 978-3-642-45567-4
eBook Packages: Springer Book Archive