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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.