Generalized Derivatives and Optimality Conditions in Nonconvex Analysis and Some Calculus Rules
Refail Kasımbeyli · 2023
Generalized derivatives play an important role in optimization. In this paper we investigate new properties of the weak subgradients and the radial epiderivatives. The weak subgradient concept has been introduced as an extension of the subgradient notion of the convex analysis and is used to investigate certain classes of nonconvex and nonsmooth optimization problems. The radial epiderivative concept has been formulated as a natural generalization of the directional derivative and is used to formulate necessary and sufficient optimality conditions for both nonconvex vector optimization and single-objective optimization problems. In this paper we investigate new properties of these concepts and give some calculus rules.