Second-Order Necessary Conditions for Set Constrained Nonsmooth Optimization Problems via Second-Order Projective Tangent Cones
Elena Constantin · LIBERTAS MATHEMATICA (new series) · 2016
We present second-order necessary optimality conditions for constrained minimization problems involving locally Lipschitz functions. We extend some second-order necessary conditions of extremum due to J.P Penot for twice Frechet differentiable objective functions subject to a constraint set given just as a set. We describe the second-order tangent sets and then the higher-order tangent sets to the null-set of a mapping between two Banach spaces. Also we characterize the higher-order adjacent sets and the related higher-order tangent cones in Pavel sense to the null-sets of such a mapping. The effectiveness of our results is illustrated on some examples.