On second-order Fritz John type optimality conditions for a class of differentiable optimization problems

Abstract

In this paper, we focus on the inequality constrained optimization problems, where the involved functions belong to the class , i.e. functions which have Lipschitz continuous gradient mappings. We propose a second-order mean value inequality for a function in terms of its limiting second-order subdifferential. By virtue of this inequality, using the second-order tangent set and the asymptotic second-order tangent cone, we establish the second-order Fritz John type necessary and sufficient optimality conditions for differentiable optimization problems with inequality and set constraints.