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

In this paper, we focus on the inequality constrained optimization problems, where the involved functions belong to the class C 1 , 1 , i.e. functions which have Lipschitz continuous gradient mappings. We propose a second-order mean value inequality for a C 1 , 1 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. [ABSTRACT FROM AUTHOR]