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# Questions tagged [semidefinite-programming]

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### Nearest positive semidefinite matrix to a symmetric matrix in the spectral norm

So I have a symmetric matrix $A$ and I would like to solve the optimization problem, $$\hspace{2.5mm}\text{Minimize}\;\; \|A-S\|_2$$ $$\hspace{-5mm}\text{Subject to}\;\; S\geq0.$$ $A$ is given and $S$ ...
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### Best platform for complex SDPs with n and m around 5-15K?

I am looking to solve a class of SDPs with complex entries, with the semi-definite cone $S^n$, $n$ around 5000 to 15000. Also, $m$, the number of equality/inequality constraints is close to $n$. I ...
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### log(det(X)) in Semidefinite Programming

I have been solving problems of the form $$max \ log(det(A)) \\ s.t. \ A = A^{T} \succeq 0, \\ p_{i}^{T}Ap_{i} \leq b_{i}$$ where $b_{i}$ and $p_{i}$ are input vectors (to be clear there is more than ...
Consider the following program: $$\max_{\pmb a} \sum_i z_i\\ u.c. \pmb a \pmb P_i\pmb a^\top\geq z_i$$ where $\pmb a \in\mathbb{R}^p$ and the $\pmb P_i$ are all symmetric positive semidefinite ...