On a Control Problem Containing Support Functions

I. Husain¹, A. Ahmed², Abdul Raoof Shah²

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

DOI: 10.4236/ajor.2014.45031                

Abstract

A control problem containing support functions in the integrand of the objective of the functional as well as in the inequality constraint function is considered. For this problem, Fritz John and Karush-Kuhn-Tucker type necessary optimality conditions are derived. Using Karush-Kuhn-Tucker type optimality conditions, Wolfe type dual is formulated and usual duality theorems are established under generalized convexity conditions. Special cases are generated. It is also shown that our duality results have linkage with those of nonlinear programming problems involving support functions.

Keywords

Control Problem, Support Function, Optimality Conditions, Generalized Convexity, Wolfe Type Duality, Nonlinear Programming Problem

Conflicts of Interest

The authors declare no conflicts of interest.

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