Quadratic programming: Difference between revisions

Revision as of 11:38, 26 February 2002

Revision as of 11:02, 14 April 2002

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Quadratic programming problem can be formulated like this:

Assume x belongs to '''R'''ⁿ space. The (n x n) [[matrix]] E is [[positive semidefinite]].

Minimize (with respect to x)

f(x) = 0.5 x' E x + f' x

with the following boundary constraints (if there exists an answer then it satisfies these):

(1) A*x <= b (inequality constraint)

(2) C*x = d (optionalequality contraint)

Since f(x) is a '''convex function''', and constraints are '''linear functions''', we have from optimization theory that for point x to be an optimum point it is necessary and sufficient that x is a Kuhn-Tucker point.

The (n x n) [[matrix]] E is usually [[positive semidefinite]].

(this article needs a lot more work..)