Continuous-time Programming

The optimization problems in the previous Chapters have all been finite dimensional and functions have been defined onRⁿand the number of constraints has been finite. However, a great deal of optimization theory is concerned with problems involving infinite dimensional normal spaces.

In this Chapter, we extend the concept of V–invexity to continuous functions and to continuous functionals and use it to obtain sufficient optimality conditions and duality results for different kinds of multiobjective variational and control problems. For this purpose the Chapter is divided in six sections. In Section 2, we extend the concept of V– invexity to continuous functions and discuss some examples. In Section 3, we present a number of Kuhn-Tucker type sufficient optimality conditions. In Section 4, Mond-Weir type duality results are obtained under avarietyofV– invexity assumptions. In Section 5, we have presented multiobjective control problems and obtained duality theorems. In last Section, we have considered a class of nondifferentiable multiobjective variational problems and establish duality results mainly for conditionally properly efficient solutions of the problem.