NEW CHARACTERIZATIONS OF WEAK SHARP AND STRICT LOCAL MINIMIZERS IN NONLINEAR PROGRAMMING
Marcin Studniarski · Communications in Optimization Theory · 2012
We consider the problem of identifying weak sharp local minimizers of order m, an important class of possibly non-isolated local minimizers. A characterization of such minimizers is obtained for a nonlinear programming problem with an abstract set constraint. The results are formulated in terms of certain normal and tangent cones to given sets, and generalized directional derivatives of the objective function. A particular case where the constraint set is given by a system of inequalities is also considered. As a consequence, we obtain a useful characterization of strict local minimizers of order m.