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

Copyright

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References

[1]	S. Chandra, B.D. Craven, and I. Husain, ‘A class of nondifferential Control problems’, J. Optim. Theory Appl. 56 (1988), 227-243.
[2]	I. Husain and Z. Jabeen, ‘Mixed duality for a Programming containing support functions’, J. Appl. Math & computing Vol. 15 (2004), No 1-2 pp. 211-225.
[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.