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Quadratic ProgrammingQuadratic programming (QP) is a special type of mathematical optimization problem. The quadratic programming problem can be formulated like this: Assume belongs to space. The () matrix is positive semidefinite and is any () vector. Minimize (with respect to ) with at least one instance of the following kind of constraints (if there exists an answer then it satisfies these): (1) (inequality constraint) (2) (equality contraint) If is positive definite then is a convex function and constraints are linear functions. We have from optimization theory that for point to be an optimum point it is necessary and sufficient that is a Karush-Kuhn-Tucker (KKT) point. If there are only equality constraints, then the QP can be solved by a linear system. Otherwise, the most common method of solving a QP is an interior point method, such as LOQO. Active set methods are also commonly used. External links
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