# Timeline for Optimization with matrix determinant as constraint

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Mar 3 '17 at 17:17 comment @FeiZhu Did you ever solve this problem?
Jun 30 '15 at 5:23 comment Generally no more than 20.
Jun 28 '15 at 6:47 history tweeted
Jun 28 '15 at 4:22 comment How many $\mathbf{E_i}$ vectors are involved?
Jun 27 '15 at 9:11 history edited
provide form of the objective function and other constraints
Jun 26 '15 at 14:10 answer timeline score: 3
Jun 5 '15 at 16:49 comment The constraint $\det A \gt 0$ is very mild. It would be helpful to know what objective function is being optimized and all the constraints so that suggestions can be more targeted.
Jun 5 '15 at 2:24 comment Indeed the gradient is numerically unstable and that's why I'm seraching for a solution that avoids naively computing the unstable gradient. $\mathbf{A}$ is 6$\times$6 in our case, and the objective is quadratic with respect to $\mathbf{A}$.
Jun 4 '15 at 20:57 comment Your formula ${\partial \mathrm{det}(\mathbf{A})}/{\partial \mathbf{A}} = \mathrm{det}(\mathbf{A})(\mathbf{A}^{-1})^T$ is numerically unstable when $\mathrm{det}(\mathbf{A})=0$: you are trying to express a finite quantity as $0\cdot\infty$, and this is not possible by naively computing the product of a small term times a very big (ill conditioned) one. Apart from the very pertinent answer by @ArnoldNeumaier, other computing strategies could be devised, if you provide some more background. How big is $\mathbf{A}$, are you trying a global or a local optimisation?
Jun 4 '15 at 15:46 answer timeline score: 4
Jun 4 '15 at 8:34 history asked