CVXOPT User’s Guide

Release 1.3.3 – February 9, 2026

Martin Andersen, Joachim Dahl, and Lieven Vandenberghe

• Copyright and License
• Introduction
• Dense and Sparse Matrices
  • Dense Matrices
  • Sparse Matrices
  • Arithmetic Operations
  • Indexing and Slicing
  • Attributes and Methods
  • Built-In Functions
  • Other Matrix Functions
  • Randomly Generated Matrices
• The BLAS Interface
  • Matrix Classes
  • Level 1 BLAS
  • Level 2 BLAS
  • Level 3 BLAS
• The LAPACK Interface
  • General Linear Equations
  • Positive Definite Linear Equations
  • Symmetric and Hermitian Linear Equations
  • Triangular Linear Equations
  • Least-Squares and Least-Norm Problems
  • Symmetric and Hermitian Eigenvalue Decomposition
  • Generalized Symmetric Definite Eigenproblems
  • Singular Value Decomposition
  • Schur and Generalized Schur Factorization
  • Example: Analytic Centering
• Discrete Transforms
  • Discrete Fourier Transform
  • Discrete Cosine Transform
  • Discrete Sine Transform
• Sparse Linear Equations
  • Matrix Orderings
  • General Linear Equations
  • Positive Definite Linear Equations
  • Example: Covariance Selection
• Cone Programming
  • Linear Cone Programs
  • Quadratic Cone Programs
  • Linear Programming
  • Quadratic Programming
  • Second-Order Cone Programming
  • Semidefinite Programming
  • Exploiting Structure
  • Optional Solvers
  • Algorithm Parameters
• Nonlinear Convex Optimization
  • Problems with Nonlinear Objectives
  • Problems with Linear Objectives
  • Geometric Programming
  • Exploiting Structure
  • Algorithm Parameters
• Modeling
  • Variables
  • Functions
  • Constraints
  • Optimization Problems
  • Examples
• C API
  • Dense Matrices
  • Sparse Matrices
• Matrix Formatting
• cvxopt.org