# Numerical Optimization#

- Knapsack Problems
- Mixed Integer Linear Programming
- Semidefinite Programming
- Linear Functions and Constraints
- Matrix/Vector-Valued Linear Functions: Parents
- Matrix/Vector-Valued Linear Functions: Elements
- Constraints on Linear Functions Tensored with a Free Module
- Numerical Root Finding and Optimization
- Interactive Simplex Method
- Gauss-Legendre Integration for Vector-Valued Functions

## Linear Optimization (LP) and Mixed Integer Linear Optimization (MIP) Solver backends#

Sage also supports, via optional packages, CBC (COIN-OR), CPLEX (ILOG), and Gurobi. In order to find out how to use them in Sage, please refer to the Thematic Tutorial on Linear Programming.

The following backend is used for debugging and testing purposes.

## Semidefinite Optimization (SDP) Solver backends#

For more details on CVXOPT, see CVXOPT documentation.