### 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

data.

Our results have been used to solve problems to which the optimality

conditions of the above mentioned authors are not applicable.