CVXOPT User’s Guide

Joachim Dahl & Lieven Vandenberghe

Release 1.0 – April 24, 2008
Copyright and License
1 Introduction
2 Dense Matrices (cvxopt.base)
 2.1 Creating Matrices
 2.2 Attributes and Methods
 2.3 Arithmetic Operations
 2.4 Indexing and Slicing
 2.5 Built-in Functions
 2.6 Other Matrix Functions
 2.7 Randomly Generated Matrices
 2.8 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 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 Matrices (cvxopt.base)
 6.1 Creating Sparse Matrices
 6.2 Attributes and Methods
 6.3 Arithmetic Operations
 6.4 Indexing and Slicing
 6.5 Built-In Functions
 6.6 Sparse BLAS Functions
7 Sparse Linear Equations
 7.1 Matrix Orderings (cvxopt.amd)
 7.2 General Linear Equations (cvxopt.umfpack)
 7.3 Positive Definite Linear Equations (cvxopt.cholmod)
 7.4 Example: Covariance Selection
8 Cone Programming (cvxopt.solvers)
 8.1 Linear Cone Programs
 8.2 Quadratic Cone Programs
 8.3 Linear Programming
 8.4 Quadratic Programming
 8.5 Second-Order Cone Programming
 8.6 Semidefinite Programming
 8.7 Exploiting Structure
 8.8 Optional Solvers
 8.9 Algorithm Parameters
9 Nonlinear Convex Optimization (cvxopt.solvers)
 9.1 General Solver
 9.2 Problems with Linear Objectives
 9.3 Geometric Programming
 9.4 Exploiting Structure
 9.5 Algorithm Parameters
10 Modeling (cvxopt.modeling)
 10.1 Variables
 10.2 Functions
 10.3 Constraints
 10.4 Optimization Problems
 10.5 Examples
A C API
 A.1 Dense Matrices
 A.2 Sparse Matrices
B Matrix Formatting (cvxopt.printing)