Examples

Tutorial examples

Short examples that illustrate basic features of CVXOPT.

• Creating matrices
• Indexing of matrices
• Numpy and CVXOPT
• Solving a linear program
• Solving a quadratic program

Book examples

Examples from the book Convex Optimization by Boyd and Vandenberghe.

• Optimal trade-off curve for a regularized least-squares problem (fig. 4.11)
• Risk-return trade-off (fig. 4.12)
• Penalty function approximation (fig. 6.2)
• Robust regression (fig. 6.5)
• Input design (fig. 6.6)
• Sparse regressor selection (fig. 6.7)
• Quadratic smoothing (fig. 6.8-6.10)
• Total variation reconstruction (fig. 6.11-6.14)
• Stochastic and worst-case robust approximation (fig. 6.15-6.16)
• Polynomial and spline fitting (fig. 6.19-6.20)
• Basis pursuit (fig 6.21-6.23)
• Least-squares fit of a convex function (fig. 6.24)
• Consumer preference analysis (fig. 6.25-6.26)
• Logistic regression (fig. 7.1)
• Maximum entropy distribution (fig. 7.2-7.3)
• Chebyshev bounds (fig. 7.6-7.7)
• Chernoff lower bound (fig. 7.8)
• Experiment design (fig. 7.9-7.11)
• Ellipsoidal approximations (fig. 8.3-8.4)
• Centers of polyhedra (fig. 8.5-8.7)
• Approximate linear discrimination (fig. 8.10-8.12)
• Linear, quadratic, and fourth-order placement (fig. 8.15-8.17)
• Floor planning example (fig. 8.20)

Custom interior-point solvers

Examples from the book chapter Interior-point methods for large-scale cone programming (pdf) by M. S. Andersen, J. Dahl, Z. Liu, L. Vandenberghe; in: S. Sra, S. Nowozin, S. J. Wright (Editors) Optimization for Machine Learning, MIT Press, 2011.

• L1-norm approximation
• L1-norm regularized least-squares
• Multiclass SVM
• Robust SVM
• SDPs with upper bounds

The code for nuclear norm approximation can be found here.

Utility functions

Useful Python scripts that are not included in the distribution.

• Generating random sparse matrices (sprandmtrx.py)

• Reading and writing Matlab mat-files (matfile.py; Python 2.7 only)

Other examples

• Using CVXOPT from C