Quadratic programming: Difference between revisions

Revision as of 10:12, 26 April 2006

Revision as of 11:34, 26 April 2006

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# ''E'''''x''' = ''d'' (equality constraint)

If ''Q'' is [[positive-definite matrix|positive definite]], then the induced feature map ''f''('''x''') is a [[convex]] [[function (mathematics)|function]] and constraints are [[linear]] functions. We know from optimization theory that for point '''x''' to be an optimum point it is necessary and sufficient that '''x''' 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 [http://www.orfe.princeton.edu/~loqo LOQO]. [[Active set]] methods are also commonly used, as well as [[Conjugate gradient method]] with projection.