2

I have the following quadratically-constrained linear program (QCLP)

$$ \begin{array}{ll} \underset {x} {\text{minimize}} & -c^T x \\ \text{subject to} & x^T Q x \leq a^2 \\ & x^T L x = 1 \end{array} $$

where $Q$ and $L$ are both symmetric positive definite matrices.

I know how to solve this problem when the 2nd constraint is absent but with the additional constraint I'm unable to get a closed form solution. Does such a solution exist? If not, are there any numerical algorithms which can exploit this problem structure?

Rodrigo de Azevedo
  • 23,788
Renganathan Subramanian
  • 21
  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Mar 02 '23 at 07:24
  • What if you relaxed the 2nd constraint and used $x^T L x \leq 1$ instead? – Rodrigo de Azevedo Mar 05 '23 at 18:50

0 Answers0