On second-order Fritz John type optimality conditions for a class of differentiable optimization problems
Min Feng, Shengjie Li · Applicable Analysis · 2019
In this paper, we focus on the inequality constrained optimization problems, where the involved functions belong to the class C1,1, i.e. functions which have Lipschitz continuous gradient mappings. We propose a second-order mean value inequality for a C1,1 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.