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396 views

Hessian of function of covariance matrices

Suppose we have a typical logdet function $\mathcal{L}$ with respect to a covariance matrix $\mathbf{A}$, $$ \mathcal{L}(\mathbf{A}) = \log\vert \mathbf{I} + \mathbf{A}\mathbf{S} \vert - ...
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137 views

SDP formulation of noisy low rank matrix completion

Exact low rank matrix completion using nuclear norm minimization can be formulated as a semidefinite program (SDP). Following the notation in the paper, a convex problem for noisy matrix completion ...
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1answer
53 views

optimization of inverse matrix with constraint on matrix elements

everyone! I have this optimization problem with constraint. D and T are symmetric matrice, where T is known and D is the unknown parameter. x and v are two known p-dimensional vectors. The objective ...
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73 views

Homotopy with non piece-wise linear boundary

in the middle of a long proof I encounter the following problem. Let $E$ be a closed and convex set in $\mathbb R^n$ such that for all $\vec x\in E$ it holds that $\sum_ix_i=1$. (We can understand ...