I have to solve a inequality constrained quadratic optimization problem.

where the objective function is $x^{T}Mx$ subject to $A x\leq b$ and $Cx=d$. In order to prove that the problem can be posed as a convex quadratic program, I need to prove M is either positive semi-definite or positive definite (for strict convexity).

M is a symmetric $n\times n$ matrix but extremely complicated in terms of variable $x$

However, I can show that for some matrix $B \in {R}^{3 \times n}$, M = $B^{T}B$ Is this enough to prove the positive semi-definiteness of $M$, I understand that since $B$ being non-square is singular, therefore the matrix $M$ cannot be positive definite. Thanks!

  • $\begingroup$ Yes, this is fine. In fact, some solvers would prefer you supply $B$ instead of $M$! $\endgroup$ Aug 8, 2016 at 18:44


You must log in to answer this question.

Browse other questions tagged .