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Dec 13, 2017 at 5:43 comment added Igor Rivin @dineshdileep Since you already state that $S$ is positive definite, I assumed that this was an extra condition.
Dec 13, 2017 at 4:43 comment added dineshdileep $S\geq 0$ is not element-wise, it implies that the matrix is positive semi-definite. Still, it is a convex problem once I consider Log-Determinant and I can use out-of-box SDP methods to solve this. However, I need to know whether $A$ and $S$ will have the same set of Eigen vectors. Going that route will also bring huge computational savings as well.
Dec 12, 2017 at 19:32 history answered Igor Rivin CC BY-SA 3.0