Duality in nonlinear programming involving semilocally convex and related functions

A nonlinear programming problem is considered where the functions involved are nondifferentiable, Fritz John type and Karush-Kuhn-Tucker type necessary optimality conditions are given in terms of the right differentials of the functions. Wolfe’s type and Mond-Weir type duals are formulated and duality results are obtained by using the concepts of semilocally quasi-convex and semilocally pseudoconvex functions.