Sufficient Conditions of Isolated Minimizers for Constrained Programming Problems
Sichen Li, Shaoyuan Xu Shaoyuan Xu · Numerical Functional Analysis and Optimization · 2010
In this article, sufficient optimality conditions for nonsmooth programming problems with inequality constraints are studied. When the objective and constraint functions are ℓ-stable at some point, a first-order sufficient optimality condition for an isolated local minimizer of order 1 is established. A second-order sufficient optimality condition for an isolated local minimizer of order 2 is obtained in terms of the lower Dini second-order directional derivatives of the Lagrangian function. The obtained results extend and improve the ones found by Ward [21 D.E. Ward ( 1994 ). Characterizations of strict local minima and nacessary conditions for weak sharp minima . Journal of Optimization Theory and Applications 80 : 551 – 571 .[Crossref], [Web of Science ®] , [Google Scholar]].