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On a complementarity problem associated with nondifferentiable programming

Published online by Cambridge University Press:  17 February 2009

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.)
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Abstract

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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
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Eaves, B. C., “On quadratic programming,” Management Sci. 17 (1971), 698711.CrossRefGoogle Scholar
[2]Kojima, M., “A unification of the existence theorems of the nonlinear complementarity problem,” Math. Programming 9 (1975), 257277.CrossRefGoogle Scholar
[3]Mahajan, D. G. and Vartak, M. N., “Generalizations of some duality theorems in nonlinear programming,” Math. Programming 12 (1977), 293317.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), 169174.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), 611613.CrossRefGoogle Scholar
[8]Parida, J. and Sahoo, B., “On the complementarity problem over polyhedral cone,” Indian J. Pure Appl. Math. 11 (1980), 838844.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), 291299.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), 380384.CrossRefGoogle Scholar