11,308 reputation
21965
bio website people.kyb.tuebingen.mpg.de/…
location Airport, USA
age
visits member for 3 years, 8 months
seen 53 mins ago

Researcher in Optimization, Machine Learning, etc.

Fan of: Inequalities, Matrix Analysis, Noncommutative polynomials, and related algebras.

I'm here to learn; if you think there's any $\epsilon$ that I might be able to say to a problem of yours, please don't hesitate to contact me.


2d
revised submatrix of a given size with maximum frobenius norm
added NP-hardness proof.
Apr
18
comment Advice for number theory library
From the title, I thought you were asking about: "The Number Theory Library" shoup.net/ntl :-)
Apr
17
comment Maximum chi-square distance between norm vectors
what's the distance between $(1,0)$ and $(0,1)$...
Apr
17
reviewed Close Information geometry divergence
Apr
16
answered submatrix of a given size with maximum frobenius norm
Apr
15
reviewed Close Gradient Estimation Using Bicubic Interpolation and Finite Differences
Apr
15
reviewed Close complexe integration around a branch point
Apr
15
reviewed Close Dead Flies Problem
Apr
15
reviewed Close Variance of the estimator of a geometric distribution
Apr
15
comment Trace of Inverse matrix from Cholesky
So you wish to compute $\mbox{trace}(L^{-T}L^{-1})$ without actually computing $L^{-1}$? You can use quadrature + randomisation based algorithms to approximate this term, but I don't know if that's what you're after....
Apr
14
comment Why do so many textbooks have so much technical detail and so little enlightenment?
A minor comment @Deane: merely do as a goal is probably ultimately not the goal! Learning how to use (which admittedly is entangled with "do") mathematics (for aesthetic, pragmatic, theoretical, or any other purposes) might be a more valid goal, no?
Apr
14
comment Minimize a strictly convex quadratic function subject to linearly equality and nonnegativity constraints in finite time?
Indeed Cristóbal: I just commented to point out one more small addition to your already nice answer :-)
Apr
14
comment Minimize a strictly convex quadratic function subject to linearly equality and nonnegativity constraints in finite time?
Cristobal: as far as I can tell, the problem posed by the OP can be solved with a method that converges at a linear rate (by passing to an ADMM procedure to "easily" handle the linear constraints).
Apr
13
comment Minimize a strictly convex quadratic function subject to linearly equality and nonnegativity constraints in finite time?
@Xims: you'll benefit greatly by reading the book: Introductory lectures on convex optimization by Yurii Nesterov --- that books a very nice introduction to oracle based complexity (upper and lower bounds); you can also have a look at Lecture 23 of my course: cs.cmu.edu/~suvrit/teach/aopt.html
Apr
13
answered About partial uniqueness of SVD
Apr
13
comment Minimize a strictly convex quadratic function subject to linearly equality and nonnegativity constraints in finite time?
@XiMS: As Brian asked: "what model of computation are you using?" Complexity analysis depends on the model of computation----the term "polynomial time" too, so it would be good to know what model. But in the commonly used oracle model, the runtimes are polynomial in the problem size for $\epsilon$-accuracy solution (depending on stuff like $1/\epsilon$, $\log(1/\epsilon)$, etc.)
Apr
8
comment Is this Hankel matrix in trace class
Thanks for catching the bug; my error lay in calling $e^{4t(i+j+1)}-1$ a rank-1 matrix --- how silly can one be!
Apr
8
comment Is this Hankel matrix in trace class
It the original Hankel matrix is PSD, then we'll immediately get $\|H\| \le e^{-4t} \le 1$, but I haven't checked if it is psd (but clearly my reasoning seems naive to me)..
Apr
8
comment Distance between two sets
@Math123: If your sets are polyhedral, then both Dykstra and alternating reflections may (in principle, but hard to quantify) converge at a linear rate, so you can "detect" when to stop. If your sets are "almost parallel" then both will slow down --- you have to experiment to see what convergence criterion works for you (in the worst case, to obtain an $\epsilon$-accurate solution, these methods may require $O(1/\epsilon)$ iterations, I think)
Apr
8
comment Distance between two sets
@Igor: to my mind the greediness of AP can make it get "stuck" (e.g., at a corner). But more basically, AP just generates sequences that converges to a feasible point (because feasibility is what it set out to solve in the first place), there is nothing in the AP which should make it converge to the "best" feasible point (unless the set of feasible points in a singleton) --- a nice example is Example 11.24 in the book: "Convex analysis and monotone operator theory..." by Bauschke and Combettes.