## Invited Session Thu.2.H 2035

#### Thursday, 13:15 - 14:45 h, Room: H 2035

**Cluster 24: Variational analysis** [...]

### Stability of constraint systems

**Chair: Rene Henrion**

**Thursday, 13:15 - 13:40 h, Room: H 2035, Talk 1**

**Alexey F. Izmailov**

Strong regularity and abstract Newton schemes for nonsmooth generalized equations

**Coauthor: Alexey S. Kurennoy**

**Abstract:**

We suggest the inverse function theorem for generalized equations, unifying Robinson's theorem for strongly regular generalized equations and Clarke's inverse function theorem for equations with locally Lipschitzian mappings. This theorem is further applied in the context of very general Newton schemes, covering, among others, some methods which are usually not regarded as Newtonian. In particular, we derive new local convergence results for the augmented Lagrangian methods applied to optimization problems with locally Lipschitzian derivatives.

**Thursday, 13:45 - 14:10 h, Room: H 2035, Talk 2**

**Rene Henrion**

On (co-)derivatives of the solution map to a class of generalized equations

**Coauthors: Alexander Kruger, Jiří Outrata, Thomas Surowiec**

**Abstract:**

This talk is devoted to the computation of (co-)derivatives of solution maps associated with a frequently arising class of generalized equations. The constraint sets are given by (not necessarily convex) inequalities for which we do not assume the linear independence of gradients. On the basis of the obtained generalized derivatives, new optimality conditions for a class of mathematical programs with equilibrium constrains are derived, and a workable characterization of the isolated calmness of the considered solution map is provided. The results are illustrated by means of examples.

**Thursday, 14:15 - 14:40 h, Room: H 2035, Talk 3**

**Marco A. Lopez**

Lower semicontinuity of the feasible set mapping of linear systems relative to their domains

**Coauthors: A. Daniilidis, M.A. Goberna, R. Lucchetti**

**Abstract:**

The talk deals with stability properties of the feasible set of linear inequality systems having a finite number of variables and an arbitrary number of constraints. Several types of perturbations preserving consistency are considered, affecting respectively, all of the data, the left-hand side data, or the right-hand side coefficients. Our analysis is focussed on (lower semi-)continuity properties of the feasible mapping confined to its effective domain, dimensional stability of the images and relations with Slater-type conditions.

The results presented here are established in a joint paper with A. Daniilidis, M.,A. Goberna, and R. Lucchetti.