Duality for a Control Problem Involving Support Functions

I. Husain¹, Abdul Raoof Shah², Rishi K. Pandey¹

¹Department of Mathematics, Jaypee University of Engineering and Technology, Guna, India.
²Department of Statistics, University of Kashmir, Srinagar, India.

DOI: 10.4236/am.2014.521330                

Abstract

Mond-Weir type duality for control problem with support functions is investigated under generalized convexity conditions. Special cases are derived. A relationship between our results and those of nonlinear programming problem containing support functions is outlined.

Keywords

Control Problem, Support Function, Generalize Convexity, Converse Duality, Nonlinear Programming

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Husain, I., Ahmad, A. and Shah, A.R. (2014) On a Control Problem with Support Functions. (Submitted for Publication)
[2]	Craven, B.D. (1978) Mathematical Programming and Control Theory. Chapman and Hall, Landon. http://dx.doi.org/10.1007/978-94-009-5796-1
[3]	Mond, B. and Hanson, M. (1968) Duality for Control Problem. SIAM Journal on Control, 6, 114-120. http://dx.doi.org/10.1137/0306009
[4]	Husain, I., Abha and Jabeen, Z. (2002) On Nonlinear Programming with Support Function. Journal of Applied Mathematics and Computing, 10, 83-99.