# S. Sra

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 Name S. Sra Member for 2 years Seen 1 hour ago Website Location Tübingen, Germany Age
Researcher in Optimization, Machine Learning, etc. Hobbyist in: Matrix Analysis
 1d revised Applications of Hilbert’s metricadded new reference 1d accepted On a version of gradient descent 1d answered How to maximize the determinant of a matrix of the form VDV^H 1d revised How to maximize the determinant of a matrix of the form VDV^H added some tags, fixed TeX and some grammar plus typos 1d comment On a version of gradient descentI tested it on a simple numerical example; the sequence $r_t$ is not monotonic. Since you essentially brought up this point, I attributed it to you. 1d revised On a version of gradient descentfixed answer 1d comment On a version of gradient descentOk, I think I was too quick!! I'll check the details of the proof tmw and update my answer. 1d comment On a version of gradient descentSorry, don't have time to type it in right now; please see (2.1.7 and 2.1.8) in the book Introductory lectures on convex optimization by Yu. Nesterov; you'll have to adapt those lemmas to the case of $f$ restricted to the $i$-th coordinate. From that the desired conclusion will follow. (Also, since $f$ is convex, $f'$ is monotone, so the inequality that you've mentioned in the comment also holds. The index being largest in magnitude was used for an earlier inequality in the cited paper. 2d answered On a version of gradient descent May13 comment Reference needed for: Automatic generation of relevant mathematical exercises (similar to ones written by human) with the help of machine learning"automatic", "relevant", "similar to ...", "mathematical" --- quite a challenging list I'd say. Maybe you could begin by creating a database of questions (taken e.g., from Polya and Szego's book)---but have you already figured out other basic issues such as: how'd you represent the input data? Maybe some work in automatic theorem proving might suggest potential automation clues.... May13 comment Convexity of polylogaritmssorry; I made a typo in my calculations! this convexity seems rather delicate because a slight change seems to make it concave...I'll think about it if I get time; May13 comment Collatz stopping-time and Poisson distribution, and connection to other problems?Did you mean "threads" or was it really "threats"? In both cases, however, the question remains the same :-) May11 comment M-matrix plus S-matrix is P-matrix?Sorry, i just mistyped the extra word "integral" there...it is of course positive definite over the reals too! May11 awarded ● Good Question May10 comment M-matrix plus S-matrix is P-matrix?@Santiago: A symmetric, nonsingular $M$-matrix is a Stieltjes matrix and a symmetric matrix over the integers is Stieltjes if and only if it is positive definite. So at least the integral counterexamples above will not extend to the case when we have symmetry (as the sum of two strictly (symmetric) positive definite matrices cannot lose rank). May10 awarded ● Nice Answer May10 awarded ● Nice Answer May10 comment M-matrix plus S-matrix is P-matrix?(but replacing the 1s by 1/4 and 3/4, in the M and S parts, respectively does the trick) May10 comment M-matrix plus S-matrix is P-matrix?Will, you forgot to add the diagonals! May9 comment What happens to Virasoro at c=25?@José: wow, so random turned out to be not entirely random---though unfortunately I am quite far from understanding the content and background that you have provided. Thanks! May8 comment Literature on Exponential of a Quadratic FormIt is neither convex nor concave (ignore for now the extra constraint that $x^Tx=1$, because with that constraint, you are asking for convexity on the surface of a hypersphere, which can at best hold only very locally); to see why, simply generate a few random vectors and test what happens to $f$. May8 comment On solution of a class of discrete-time Lyapunov equation Also note that if $\|\sum_i F_i \kron F_i\| < 1$, then starting from $X_0=I$, you can iterate $X_{k+1} = \sum_i F_iX_kF_i^T + C$, and converge to the unique semidefinite solution. If the operators don't satisfy this sufficient condition, then more thought is needed. May8 comment On solution of a class of discrete-time Lyapunov equation Ah, so you are asking whether $\text{mat}(x)$ will be positive semidefinite? Well, if the original linear system has a unique solution that is guaranteed to be semidefinite, then by solving the vectorized linear system, we should end up recovering that. It remains to determine conditions under which the original system has a semidefinite solution. The above system seems to me to be a well-studied problem; hopefully, F. Poloni (on MO) takes a look and provides some more details, as I think he knows more about these things. May8 accepted On solution of a class of discrete-time Lyapunov equation May8 comment What happens to Virasoro at c=25?Are these objects related to bosonic string theory with its $25+1$ space-time dimension (sorry, random pattern matching content free comment) :-) May7 answered On solution of a class of discrete-time Lyapunov equation May3 comment Uniqueness of fixed points for rational transformationsI kept everything strictly positive to not have to deal with infinities and potentially unbounded derivatives of $\log$---but with care, usually one can get away :-) May2 accepted Uniqueness of fixed points for rational transformations May1 comment Norms on tensor productsto get some comparison inequalities, you might benefit from searching for Pisier's survey on Grothendieck inequalities... Apr30 answered Uniqueness of fixed points for rational transformations Apr29 comment Number of Distinct Sums of Integersthis sounds like an arithmetic combinatorics problem.... Apr28 comment how do you call a function that satisfies the metric axioms except for the coincidence axiom?One example would be: $d(x,y) := \delta(x,y)+\delta(x,a)+\delta(y,b)$, where $\delta(x,y)$ is a usual metric, and $a \neq b$ are two arbitrary points in space (to have an example slightly less trivial than $d(x,y) := \delta(x,y) + \epsilon$... Apr28 comment how do you call a function that satisfies the metric axioms except for the coincidence axiom?Hi Marco: I'd call these distances "strictly positive definite" but that sounds like mixing up terms. Apr28 revised A spectral inequality for positive-definite matrices fixed stupid error Apr28 comment A spectral inequality for positive-definite matrices Oops, sorry, you are right, it should be $nM^2-m^2$! When typing it up, I felt the $\sqrt{M}$ factor to be a bit odd. Let me update the answer! Thanks. Apr28 accepted A spectral inequality for positive-definite matrices Apr28 comment Toolbox for directed graphswrong forum in my opinion; you might want to try stats.stackexchange Apr27 answered A spectral inequality for positive-definite matrices Apr26 comment Fast way of finding RSS of Multiple Linear Regressionmathoverflow.net/howtoask Apr26 comment Finding a sub-matrix from a fat matrix with the best condition number.seems to be a duplicate of: mathoverflow.net/questions/104803/… Apr26 answered Finding a sub-matrix from a fat matrix with the best condition number. Apr25 answered iteratively (approximately) solving a sum of exponentials Apr24 comment Constraint optimization problem for any dimensionality $n>1$.@Mark: maybe, though here I think first it'll be good to see how these constraints can be combined to yield a simpler problem---the cubic constraint is the troublesome one...) Apr24 comment Constraint optimization problem for any dimensionality $n>1$.yes, i know that it is not "the" :-) --- (the second largest eigenvalue occurs twice) Apr23 answered Constraint optimization problem for any dimensionality $n>1$. Apr22 comment Global maximum of non-concave functionThere are several possible maxima it seems. Consider, e.g., for $f_1$, that $x_1=x_6=1/2$ and all other $x$s are zero. Then, $f_1=1$; same value is also achieved by your choice of $x_i=1/6$. Or are you asking whether for an optimum we can always pick a uniform vector? This might follows from the cyclic symmetry of your function, or the other kinds of symmetry groups that these functions are encoding. Apr22 comment Another identity involving sums of (alternating) binomial coefficients.@Todd: Oren Patashnik is the name; also, that's the guy who (co-)made BibTeX, so .... :-) Apr22 comment What are the most important open problems in algebraic combinatorics?in any case, this should be made community wiki... Apr22 comment The eigenvalues of the product of two matrices @Douglas: ok, I think in my comment the word "any" was meant in a colloquial style to mean "pretty much any trivial", rather than in a mathematically precise sense! Apr19 revised Ratio sum comparison on operatorsupdated the reflect that an alleged solution was wrong.