I have an optimization problem which is described as $$\begin{array}{ll} \text{minimize}_x & c^{T}x\\ \text{subject to} & Gx \preceq h\\ & -x^{T}Px - qx - r \leq 0 \end{array} $$ where $P$ is positive semi-definite.

Is there any way to convert this problem into a convex problem?

  • 2
    $\begingroup$ No, there is not. See this PDF for some heuristic alternatives. $\endgroup$ – Michael Grant Nov 3 '14 at 16:52

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