CVXOPT User’s Guide

Joachim Dahl & Lieven Vandenberghe

Release 1.1 – October 15, 2008
Copyright and License
1 Introduction
2 Dense and Sparse Matrices
 2.1 Dense Matrices
 2.2 Sparse Matrices
 2.3 Arithmetic Operations
 2.4 Indexing and Slicing
 2.5 Attributes and Methods
 2.6 Built-In Functions
 2.7 Other Matrix Functions
 2.8 Randomly Generated Matrices
 2.9 The NumPy Array Interface
3 The BLAS Interface (cvxopt.blas)
 3.1 Matrix Classes
 3.2 Level 1 BLAS
 3.3 Level 2 BLAS
 3.4 Level 3 BLAS
4 The LAPACK Interface (cvxopt.lapack)
 4.1 General Linear Equations
 4.2 Positive Definite Linear Equations
 4.3 Symmetric and Hermitian Linear Equations
 4.4 Triangular Linear Equations
 4.5 Least-Squares and Least-Norm Problems
 4.6 Symmetric and Hermitian Eigenvalue Decomposition
 4.7 Generalized Symmetric Definite Eigenproblems
 4.8 Singular Value Decomposition
 4.9 Schur and Generalized Schur Factorization
 4.10 Example: Analytic Centering
5 Discrete Transforms (cvxopt.fftw)
 5.1 Discrete Fourier Transform
 5.2 Discrete Cosine Transform
 5.3 Discrete Sine Transform
6 Sparse Linear Equations
 6.1 Matrix Orderings (cvxopt.amd)
 6.2 General Linear Equations (cvxopt.umfpack)
 6.3 Positive Definite Linear Equations (cvxopt.cholmod)
 6.4 Example: Covariance Selection
7 Cone Programming (cvxopt.solvers)
 7.1 Linear Cone Programs
 7.2 Quadratic Cone Programs
 7.3 Linear Programming
 7.4 Quadratic Programming
 7.5 Second-Order Cone Programming
 7.6 Semidefinite Programming
 7.7 Exploiting Structure
 7.8 Optional Solvers
 7.9 Algorithm Parameters
8 Nonlinear Convex Optimization (cvxopt.solvers)
 8.1 Problems with Nonlinear Objectives
 8.2 Problems with Linear Objectives
 8.3 Geometric Programming
 8.4 Exploiting Structure
 8.5 Algorithm Parameters
9 Modeling (cvxopt.modeling)
 9.1 Variables
 9.2 Functions
 9.3 Constraints
 9.4 Optimization Problems
 9.5 Examples
A C API
 A.1 Dense Matrices
 A.2 Sparse Matrices
B Matrix Formatting (cvxopt.printing)