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We consider the problem of identifying weak sharp local minimizers of order m, an importantclass of possibly non-isolated local minimizers. A characterization of such minimizers is obtained for anonlinear programming problem with an abstract set constraint. The results are formulated in terms ofcertain normal and tangent cones to given sets, and generalized directional derivatives of the objectivefunction. 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.
How to Cite this Article:
Marcin Studniarski, New characterizations of weak sharp and strictlocal minimizers in nonlinear programming, Communications in Optimization Theory 1 (2012), 19-34.