LIPSCHITZ r-INVEX FUNCTIONS AND NONSMOOTH PROGRAMMING

ABSTRACT

In the paper, a family of real Lipschitz functions, called r-invex, which represents a generalization of the notion of invexity is introduced. The principal analytic tool is the generalized gradient of Clarke for Lipschitz functions. Furthermore, under appropriate r-invexity assumptions, necessary optimality conditions of the Slater type and sufficient optimality conditions are obtained for a nonsmooth programming problem. Also some duality results are obtained for such problems.

Keywords:

• Lipschitz function
• Clarke's generalized gradient
• r-Invex function
• Nonsmooth programming

Acknowledgments