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visits member for 2 years, 1 month
seen Feb 16 at 23:05

I work on the computer vision behind augmented reality applications for mobile phones at a startup called Ogmento in New York City.


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.
Apr
3
asked Distance between two points in UTM coordinates.