While generalized equations with differentiable single-valued base mappings and the associated Josephy–Newton method have been studied extensively, the setting with semismooth base mapping had not been previously considered (apart from the two special cases of usual nonlinear equations and of Karush-Kuhn-Tucker optimality systems). We introduce for the general semismooth case appropriate notion...

We prove that the notion of KT-invexity for continuous-time nonlinear optimization problem is a necessary and sufficient condition for global optimality of a KarushKuhn-Tucker point.

This paper presents an asymptotic analysis of a Monte Carlo method, variously known as sample average approximation (SAA) or sample path optimization (SPO), for a general two-stage stochastic minimization problem. We study the case when the second-stage problem may have multiple local optima or stationary points that are not global solutions and SAA is implemented using a general nonlinear prog...

The majority of research on bilevel programming has centered on the linear version of the problem in which only one leader and single follower are involved. This paper proposes a general model and Kuhn-Tucker approach for linear bilevel programming problems in which one leader and multiple follower(s) are involved, and there may (not) be sharing variables among the followers. Finally, a numeric...

We study the smoothing method for the solution of generalized semi-infinite optimization problems from (O. Stein, G. Still: Solving semi-infinite optimization problems with interior point techniques, SIAM J. Control Optim., 42(2003), pp. 769–788). It is shown that Karush-Kuhn-Tucker points of the smoothed problems do not necessarily converge to a Karush-Kuhn-Tucker point of the original problem...

Within a Kuhn-Tucker cavity method introduced in a former