ON THE WEAK SUBDIFFERENTIAL, AUGMENTED NORMAL CONES AND DUALITY IN NONCONVEX OPTIMIZATION

This article studies the properties of the weak subdifferential for nonsmooth and nonconvex analysis studied. This study presents a formulation that is directly involved in convex analysis carried out in the nonconvex case. In this work, we present a theory that applies epigraphs to obtain augmented normal cones. The perturbation function plays a crucial role in establishing optimality conditions. This study demonstrates that positively homogeneous and lower semicontinuous functions are weakly subdifferentiable. Moreover, under specific conditions related to the objective function, the constraint function, and the feasible set, we show that the perturbation function is positively homogeneous. Thus we obtain a zero duality gap condition by implementing conditions on the objective function, constraint functions, and the set S.