r-preinvexity and r-invexity in mathematical programming

In the paper, we introduce and characterize a new class of nonconvex functions in mathematical programming, named r-preinvex functions, which are called r-invex functions in the case of differentiability. The class of r-preinvex functions is wider than that of preinvex functions and thus, in the case of differentiability, than the class of invex functions. Some optimality results are obtained under r-preinvexity assumption for a constrained optimization problem with not necessarily differentiable functions. Further, a number of sufficiency conditions and Wolfe duality theorems are established under r-invexity assumption. An alternative approach with a modified r-invexity notion to optimality conditions and duality results is also considered. (c) 2005 Elsevier Ltd. All rights reserved.