Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-18T20:33:32.715Z Has data issue: false hasContentIssue false
  • English
  • Français

On a complementarity problem associated with nondifferentiable programming

Published online by Cambridge University Press:  17 February 2009

B. D. Craven ,
B. Mond  and
J. Parida
B. D. Craven
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria3052
B. Mond
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria3083.
J. Parida
Affiliation:
Department of Mathematics, Regional Engineering College, Rourkela 769 008, India. (The contribution of this author was made while he was a visitor to the University of Melbourne.)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper deals with the question of the existence of a solution to the stationary-point problem corresponding to a given nonlinear nondifferentiable program. An existence theorem for the stationary-point problem is presented under some convexity and regularity conditions on the functions involved, which also guarantee an optimal solution to the nonlinear program.

Type
Research Article
Information
The ANZIAM Journal , Volume 25 , Issue 3 , January 1984 , pp. 419 - 430
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Eaves, B. C., “On quadratic programming,” Management Sci. 17 (1971), 698–711.CrossRefGoogle Scholar
[2]Kojima, M., “A unification of the existence theorems of the nonlinear complementarity problem,” Math. Programming 9 (1975), 257–277.CrossRefGoogle Scholar
[3]Mahajan, D. G. and Vartak, M. N., “Generalizations of some duality theorems in nonlinear programming,” Math. Programming 12 (1977), 293–317.CrossRefGoogle Scholar
[4]Mangasarian, O. L., Nonlinear programming (McGraw-Hill, New York, 1969).Google Scholar
[5]Mond, B., “A class of nondifferentiable mathematical programming problems,” J. Math. Anal. Appl. 46 (1974), 169–174.CrossRefGoogle Scholar
[6]Mond, B. and Panda, J., “Existence theory for programming and associated complementarity problems,” Pure Mathematics Research Paper No. 81–15, 08 1981, La Trobe University, Melbourne, Australia.Google Scholar
[7]Mond, B. and Schechter, M., “On a constraint qualification in a nondifferentiable programming problem,” Naval Res. Logist. Quart. 23 (1976), 611–613.CrossRefGoogle Scholar
[8]Parida, J. and Sahoo, B., “On the complementarity problem over polyhedral cone,” Indian J. Pure Appl. Math. 11 (1980), 838–844.Google Scholar
[9]Riesz, F. and Sz.-Nagy, B.. Functional analysis (translated from the 2nd French edition by Boron, L. F.). (Frederick Ungar Publishing Co., New York, 1955).Google Scholar
[10]Singh, C., “A system of inequalities and nondifferentiable mathematical programming,’ J. Optim. Theory Appl. 27 (1979), 291–299.CrossRefGoogle Scholar
[11]Sinha, S. M., “Stochastic programming,” Research Report No. 22, Operations Research Cener, University of California, Berkeley (1963).Google Scholar
[12]Sinha, S. M., “An extension of a theorem on supports of a convex function,” Management Sci. 12 (1966), 380–384.CrossRefGoogle Scholar