SMCP

Python Extension for Sparse Matrix Cone Programs

SMCP is a software package for solving linear sparse matrix cone programs. The code is experimental and it is released to accompany the following research paper:

M. S. Andersen, J. Dahl, and L. Vandenberghe, Implementation of nonsymmetric interior-point methods for linear optimization over sparse matrix cones. Submitted to Mathematical Programming Computation, Aug. 2009.

The package provides an implementation of a nonsymmetric interior-point method which is based on chordal matrix techniques. Only one type of cone is used, but this cone includes the three canonical cones — the nonnegative orthant, the second-order cone, and the positive semidefinite cone — as special cases. The efficiency of the solver depends not only on the dimension of the cone, but also on its structure. Nonchordal sparsity patterns are handled using chordal embedding techniques.

In its current form, SMCP is implemented in Python and C, and it relies on the Python extensions CHOMPACK and CVXOPT for most computations.

Current release

Version 0.2a includes:

• Nonsymmetric interior-point method (primal and dual scaling methods)
• Extended self-dual embedding
• Two KKT system solvers: one solves the symmetric indefinite augmented system and the other solves the positive definite system of normal equations
• Read/write routines for SDPA sparse data files (‘dat-s’).
• Simple interface to CVXOPT SDP solver

Future releases

We plan to turn SMCP into a C library with Python and Matlab interfaces. Future releases may include additional functionality as listed below:

• Explicitly handle free variables
• Iterative solver for the KKT system
• Automatic selection of KKT solver and chordal embedding technique
• Infeasible start solver (i.e. without self-dual embedding)

Availability

A platform-independent source package is available from the Download and installation section. The package includes source code, documentation, and installation guidelines.

Authors

SMCP is developed by Martin S. Andersen (msa@ee.ucla.edu), as PhD work under Lieven Vandenberghe at University of California, Los Angeles. The independent packages CVXOPT and CHOMPACK, which are included in the SMCP distribution, are developed by Joachim Dahl and Lieven Vandenberghe.

Feedback and bug reports

We welcome feedback, and bug reports are much appreciated. Please email bug reports to msa@ee.ucla.edu along with the following information:

• Error message (if any)
• SMCP version
• Python version
• Operating system