Talk:Quadratically constrained quadratic program
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Quadratic Programming
[edit]Is this not the same as Quadratic programming? 68.174.98.161 22:57, 9 August 2007 (UTC)
- In quadratic programming, the constraints are linear. Here, they are quadratic. -- Jitse Niesen (talk) 00:33, 10 August 2007 (UTC)
- Oh, I see.. Thanks! 68.174.98.161 18:31, 15 August 2007 (UTC)
The statement "If P0, … Pm are all positive semidefinite then the problem is convex." is correct, but the link to the convex set is somewhat misleading. A convex program is not quite the same as a convex set.
The statement "If these matrices are neither positive or negative semidefinite, the problem is non-convex" is technically correct but quite misleading. Apart from trivial cases, if a single matrix is not positive semidefinite then the problem is nonconvex. —Preceding unsigned comment added by Alexander.mitsos (talk • contribs) 14:36, 1 November 2010 (UTC)
Equality Constraints
[edit]I am still not able to verify this, but as far as I can understand, even though equality constraints can be written in the format required by QCQP and (at least for some cases) satisfy the semi-definiteness restriction, they make the problem non-convex. If such can be verified, this exception should definitely be included in the text. Since I cannot find references to this I have posted a question here: https://math.stackexchange.com/questions/1602137/quadratic-equality-constrained-quadratic-program-and-convexity
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Ax=b unexplained
[edit]The constraint Ax=b is unclear here: are A and b just any two vectors? But then one could just pick any matrix for A and vector for b. They don't occur anywhere else in the constraints.
I guess they are given, but that could be made clearer.