gcsopt 0.1.2

Library for solving optimization problems over Graphs of Convex Sets (GCS).

GCSOPT

Python library to solve optimization problems in Graphs of Convex Sets (GCS). For a detailed description of the algorithms implemented implemented in this library see the PhD thesis Graphs of Convex Sets with Applications to Optimal Control and Motion Planning . (Please note that the library recently changed name, and in the thesis it is called gcspy.)

Main features

• Uses the syntax of CVXPY for describing convex sets and convex functions.
• Provides a simple interface for assembling your graphs.
• Interface with state-of-the-art solvers via CVXPY.

Installation

You can install the latest release from PyPI:

pip install gcsopt

To install from source:

git clone https://github.com/TobiaMarcucci/gcsopt.git
cd gcsopt
pip install .

Example

Here is a minimal example of how to use gcsopt:

import cvxpy as cp
from gcsopt import GraphOfConvexSets

# Initialize empty directed graph.
G = GraphOfConvexSets(directed=True)

# Add source vertex with circular set.
s = G.add_vertex("s")
xs = s.add_variable(2)
cs = [-2, 0] # Center of the source circle.
s.add_constraint(cp.norm2(xs - cs) <= 1)

# Add target vertex with circular set.
t = G.add_vertex("t")
xt = t.add_variable(2)
ct = [2, 0] # Center of the target circle.
t.add_constraint(cp.norm2(xt - ct) <= 1)

# Add edge from source to target.
e = G.add_edge(s, t)
e.add_cost(cp.sum_squares(xt - xs))

# Solve shortest path problem from source to target.
G.solve_shortest_path(s, t)
print("Problem status:", G.status)
print("Optimal value:", G.value)
print("Optimal solution:")
print("xs =", xs.value)
print("xt =",xt.value)

The otput of this script is:

Problem status: optimal
Optimal value: 4.0
Optimal solution:
xs = [-1.  0.]
xt = [1. 0.]

License

This project is licensed under the MIT License.

Author

Developed and maintained by Tobia Marcucci.