Second-Order Necessary Conditions in Locally Lipschitz Scalar Optimization with Inequality Constraints

Friday, February 26, 2016 - 12:00 to 12:50
427 Thackeray
Speaker Information
Elena Constantin
Associate Professor
University of Pittsburgh - Johnstown

Abstract or Additional Information

The goal of this talk is to give some second-order necessary conditions
for a local minimizer and for an isolated local minimizer of order two for a
scalar mathematical programming problem with inequality constraints.

We derived our conditions without assuming any constraint qualifications
and any kind of regularity or differentiability of any of the functions consid-
ered. The objective function and the active constraint functions are only
locally Lipschitz. Thus we generalized second-order necessary optimality
conditions of A. Ben-Tal given for scalar problems with twice differentiable
data, of I. Ginchev and V.I. Ivanov and of V.I. Ivanov given for scalar prob-
lems with continuously differentiable data, and of V.I. Ivanov given for scalar
problems with locally Lipschitz and second-order Hadamard differentiable

Our results have been used to solve problems to which the optimality
conditions of the above mentioned authors are not applicable.