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pycvxset: A Python package for convex set manipulation

Abraham P. Vinod

TL;DR

This paper introduces pycvxset, a new Python package to manipulate and visualize convex sets, and uses CVXPY to solve various convex programs arising in set operations, and uses pycddlib to perform vertex-halfspace enumeration.

Abstract

This paper introduces pycvxset, a new Python package to manipulate and visualize convex sets. We support polytopes and ellipsoids, and provide user-friendly methods to perform a variety of set operations. For polytopes, pycvxset supports the standard halfspace/vertex representation as well as the constrained zonotope representation. The main advantage of constrained zonotope representations over standard halfspace/vertex representations is that constrained zonotopes admit closed-form expressions for several set operations. pycvxset uses CVXPY to solve various convex programs arising in set operations, and uses pycddlib to perform vertex-halfspace enumeration. We demonstrate the use of pycvxset in analyzing and controlling dynamical systems in Python. pycvxset is available at https://github.com/merlresearch/pycvxset under the AGPL-3.0-or-later license, along with documentation and examples.

pycvxset: A Python package for convex set manipulation

TL;DR

This paper introduces pycvxset, a new Python package to manipulate and visualize convex sets, and uses CVXPY to solve various convex programs arising in set operations, and uses pycddlib to perform vertex-halfspace enumeration.

Abstract

This paper introduces pycvxset, a new Python package to manipulate and visualize convex sets. We support polytopes and ellipsoids, and provide user-friendly methods to perform a variety of set operations. For polytopes, pycvxset supports the standard halfspace/vertex representation as well as the constrained zonotope representation. The main advantage of constrained zonotope representations over standard halfspace/vertex representations is that constrained zonotopes admit closed-form expressions for several set operations. pycvxset uses CVXPY to solve various convex programs arising in set operations, and uses pycddlib to perform vertex-halfspace enumeration. We demonstrate the use of pycvxset in analyzing and controlling dynamical systems in Python. pycvxset is available at https://github.com/merlresearch/pycvxset under the AGPL-3.0-or-later license, along with documentation and examples.

Paper Structure

This paper contains 25 sections, 11 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Set representations and operations
  3. Set representations
  4. Set operations
  5. The pycvxset package
  6. Set definitions
  7. Polytope
  8. Constrained zonotope
  9. Ellipsoid
  10. Visualizing polytopes and polytopic approximations
  11. Set operations
  12. Involving another vector $v$ and/or matrix $M$
  13. Centering
  14. Other set-specific manipulations/computations
  15. Involving another set $Y$
  16. ...and 10 more sections

Figures (9)

  • Figure 1: Plotting various sets using pycvxset.
  • Figure 2: Well-separated vectors on a $3$-dimensional unit sphere.
  • Figure 3: Projection of a point on a polytope
  • Figure 4: Centering for a polytope and a constrained zonotope.
  • Figure 5: Projection of a $3$-dimensional unit $\ell_1$-norm ball.
  • ...and 4 more figures