Alex Flint
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 Sep 2 awarded Notable Question Jan 20 comment Eliminating variables from an SOCP It seems to me that if $C$ is the feasible set for $x$ in the original problem, then $D = \{x_2:\exists x_1, (x_1,x_2) \in C\}$ is convex. Then define $f(x_2) = \min_{x_2} w^T(x_1,x_2)$ and minimizing $f$ over $D$ should yield $x_2$. The question is now whether $f$ is convex. Jan 19 comment Eliminating variables from an SOCP Fair point. But what if we're restricted to formulating the problem in terms of $w, A_i, b_i, c_i, d_i$ (and specifically not in terms of the solution $x^*$) Jan 19 comment Eliminating variables from an SOCP @MichaelGrant: The question is, if the solution to the original problem is $x^* = (x_1^*, x_2^*)$, is there any convex problem (no matter how different from the original problem) over $x_2$ such that the solution to this new problem equals $x_2^*$. Jan 19 asked Eliminating variables from an SOCP Jan 19 comment SOCP with a norm constraint This is very helpful, thank you. Jan 19 accepted SOCP with a norm constraint Jan 13 awarded Popular Question Jan 5 awarded Curious Jan 4 asked SOCP with a norm constraint Sep 24 awarded Autobiographer Jul 23 awarded Commentator Jul 23 comment Software tools for medium-scale systems of polynomial equations @wonko Each $f(x)$ is a polynomial so yes twice differentiable but not convex. Each $f(x)$ has total degree 7 or lower. The code to generate the problem is here: bit.ly/WCYM0H. A numerical dump of the cost function is here: bit.ly/1qA2kOp. Jul 23 comment Software tools for medium-scale systems of polynomial equations @wonko Thanks for the NEOS link - I was not aware of that service before. I would certainly value your help with this optimization problem (thanks!), and I'm happy to provide more details. I'm attempting to solve a problem in visual inertial navigation where the variables represent the trajectory of a device and the cost terms are related to sensor measurements captured over time by that device. Each term of the cost function looks like $(f(x)-y)^2$ where $y$ is a sensor measurement. There are no constraints on the variables except that they must be real numbers. Jul 22 comment Software tools for medium-scale systems of polynomial equations @wonko I am very much interested in global optimization rather than gradient-based iterative optimization in this problem. Methods like Gauss-Newton / Levenberg-Marquardt will not work. Having said that, are there any general purpose global optimization tools you would recommend? Jul 22 comment Solve Multivariate Polynomial How about action matrix methods where you compute a multiplication matrix and find its eigenvalues? Do you consider these as part of Grobner basis methods? Jul 22 revised Software tools for medium-scale systems of polynomial equations minor typo Jul 22 asked Software tools for medium-scale systems of polynomial equations Apr 7 awarded Scholar Apr 7 accepted Distance between two points in UTM coordinates.