Generalized Duality for a Nondifferentiable Control Problem

I. Husain^1, , Vikas K. Jain¹ and Abdul Raoof Shah²

¹Department of Mathematics, Jaypee University of Engineering and Technology, Guna, India

²Department of Statistics, University of Kashmir, Srinagar, India

Cite this paper:
I. Husain, Vikas K. Jain and Abdul Raoof Shah. Generalized Duality for a Nondifferentiable Control Problem. American Journal of Applied Mathematics and Statistics. 2014; 2(4):193-202. doi: 10.12691/ajams-2-4-3

Abstract

A generalized dual to a control problem containing support functions is formulated and various duality theorems are established under generalized convexity hypotheses. This dual model represents the combination of Wolfe and Mond-Weir type dual models to the control problem and hence it is described as a generalized dual. Some special cases are obtained. A close relationship of duality results with those of the nonlinear programming problems involving support functions is indicated.

Keywords:
control problem support function optimality conditions generalized duality converse duality nonlinear programming

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References:

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[3]	I. Husain, A. Ahmad and Abdul Raoof Shah, ‘On a control problem with support functions’, submitted for publication.
[4]	I. Husain, Abdul Raoof Shah and Rishi K. Pandey, ‘Duality for a control Problem with support function’, submitted for publication.
[5]	B. Mond and M. Hanson, ‘Duality for control problem’, SIAM J. Control 6 (1968), 114-120.