Inclusion conditions for the Constrained Polynomial Zonotopic case

TL;DR

This paper introduces new nonlinear encoding methods for inclusion testing of constrained polynomial zonotopes, enhancing their integration into optimization frameworks for complex, non-convex geometric set operations.

Contribution

It presents novel nonlinear encodings that enable efficient inclusion testing and integration of constrained polynomial zonotopes into optimization processes.

Findings

Proposed nonlinear encodings for inclusion testing.

Enhanced algebraic structure for non-convex set operations.

Facilitated integration of CPZs into optimization frameworks.

Abstract

Set operations are well understood for convex sets but become considerably more challenging in the non-convex case due to the loss of structural properties in their representation. Constrained polynomial zonotopes (CPZs) offer an effective compromise, as they can capture complex, typically non-convex geometries while maintaining an algebraic structure suitable for further manipulation. Building on this, we propose novel nonlinear encodings that provide sufficient conditions for testing inclusion between two CPZs and adapt them for seamless integration within optimization frameworks.