Alex Flint
Reputation
Next privilege 250 Rep.
 Jan20 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. Jan19 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 $x^*$) Jan19 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 $x_2^*$. Jan19 asked Eliminating variables from an SOCP Jan19 comment SOCP with a norm constraint This is very helpful, thank you. Jan19 accepted SOCP with a norm constraint Jan13 awarded Popular Question Jan5 awarded Curious Jan4 asked SOCP with a norm constraint Sep24 awarded Autobiographer Jul23 awarded Commentator Jul23 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. Jul23 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. Jul22 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? Jul22 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? Jul22 revised Software tools for medium-scale systems of polynomial equations minor typo Jul22 asked Software tools for medium-scale systems of polynomial equations Apr7 awarded Scholar Apr7 accepted Distance between two points in UTM coordinates. Apr3 asked Distance between two points in UTM coordinates.