# Solution analysis for a class of set-inclusive generalized equations: a convex analysis approach

## TL;DR

This paper uses convex analysis to study the solution sets of set-inclusive generalized equations, establishing existence conditions, error bounds, and characterizations of the solution set's geometry, especially when the set-valued term is concave.

## Contribution

It introduces new convex analysis techniques for analyzing solution existence, error bounds, and geometric properties of set-inclusive generalized equations with concave set-valued terms.

## Key findings

- Established conditions for solution existence.
- Derived global error bounds.
- Provided a characterization of the contingent cone.

## Abstract

In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the case the set-valued term appearing in the generalized equation is concave. A functional characterization of the contingent cone to the solution set is provided via directional derivatives. Specializations of these results are also considered when outer prederivatives can be employed.