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For questions on quadratic programming, methods to solve them and related solvers. Use this tag along with (optimization).

Quadratic programming is the procedure of finding the maxima/minima of a multivariate quadratic function subject to linear constraints.

For $n$ variables and $m$ constraints, the objective is find an $n\times1$ vector $\bf x$ that minimizes $\frac12{\bf x}^TQ{\bf x}+{\bf c}^T{\bf x}$ subject to $A{\bf x}\preceq{\bf b}$ where, in the real numbers,

  • $\bf c$ is an $n\times1$ vector

  • $\bf b$ is an $m\times1$ vector

  • $Q$ is an $n\times n$ symmetric matrix

  • $A$ is an $m\times n$ matrix.

Common methods to solve them include the Augmented Lagrangian and Conjugate Gradients.