## Sufficient conditions of isolated minimizers for constrained programming problems.(English)Zbl 1218.90214

Authors’ abstract: “In this article, sufficient optimality conditions for nonsmooth programming problems with inequality constraints are studied. When the objective and constraint functions are $$\ell$$-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 D. E. Ward [J. Optimization Theory Appl. 80, No. 3, 551–572 (1994; Zbl 0797.90101)].”

### MSC:

 90C46 Optimality conditions and duality in mathematical programming 90C30 Nonlinear programming

Zbl 0797.90101
Full Text:

### References:

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