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Nonlinear objectives, nonlinear constraints, non-convex objective, non-convex feasible region.

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Optimization problem involving matrix

I am struggling to solve an optimization problem of the following form: $$\begin{array}{ll} \underset{A}{\text{maximize}} & \log \det (A) \\ \text{subject to} & a^T A^{-1} a \le b\end{array}$$ Is ther …
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