20 reputation
6
bio website
location
age
visits member for 3 years, 5 months
seen Feb 8 '13 at 15:53

Aug
18
awarded  Popular Question
Sep
29
comment Linear programming - uniqueness of optimal solution
Yes, I need any vertex of the polytope due to its properties that I want to use: at every vertex there are at least d constraints that hold with equality.
Sep
28
comment Linear programming - uniqueness of optimal solution
OK, so it does not suit to me... What I need is a vertex (even any vertex). Thank you in any case!
Sep
28
comment Linear programming - uniqueness of optimal solution
Brendan, only now I realized that the last comment was yours. So, thank you too for the help!
Sep
28
accepted Linear programming - uniqueness of optimal solution
Sep
28
comment Linear programming - uniqueness of optimal solution
Thanks a lot Igor, I think this will solve my problem.
Sep
28
awarded  Commentator
Sep
28
awarded  Supporter
Sep
28
comment Linear programming - uniqueness of optimal solution
Thank you Survit, I'll look at this paper. But can I be sure that returned solution (with the smallest L-2 norm) will be a vertex of the original polytope?
Sep
28
comment Linear programming - uniqueness of optimal solution
Igor, thanks. You mean iterating the ellipsoid with any objective every time? In that case, every iteration will lead to decrease in dimension (at least one constraint will hold with equality), so finally I'll end with dimension 0, i.e., vertex. Correct?
Sep
28
asked Linear programming - uniqueness of optimal solution
Nov
12
comment Open Jackson network with deterministic arrivals.
I mean the following: service time at every queue is distributed exponentially, and the external arrivals to the system are coming at fixed intervals (i.e., instead of Poisson($\lambda$), arrivals occur at fixed time interval of $\tfrac{1}{\lambda}$). The time is continuous. Thank you.
Nov
11
asked Open Jackson network with deterministic arrivals.
Nov
7
accepted Probability Theory, Chernoff Bounds, Sum of Independent (but not identically distributed) r.v.
Nov
7
comment Probability Theory, Chernoff Bounds, Sum of Independent (but not identically distributed) r.v.
This is what I wrote in the last comment of the previous answer. So, in general, if the variables are not identical, the sum is not strongly concentrated around the $E[X]$ if $E[X]=\Theta(n)$. Thanks a lot!
Nov
6
awarded  Student
Nov
6
revised Probability Theory, Chernoff Bounds, Sum of Independent (but not identically distributed) r.v.
added 38 characters in body
Nov
6
comment Probability Theory, Chernoff Bounds, Sum of Independent (but not identically distributed) r.v.
Maybe I should write this in the question: Yes, my $E[X]=\Theta(n)$. As I commented in the another answer, I think there is no such bound for this case (linear expectation and exponential bound).
Nov
6
comment Probability Theory, Chernoff Bounds, Sum of Independent (but not identically distributed) r.v.
I mean, $X_n$ is distributed Geom($p=\tfrac{1}{n}$)
Nov
6
comment Probability Theory, Chernoff Bounds, Sum of Independent (but not identically distributed) r.v.
I think now that there is no such a bound. For example, if $X_1,...,X_{n-1}$ are distributed Geom(p=1), and $X_n$ is distributed $X_n$. Then, $E[X]=(n-1)\cdot 1 + n\approx 2n$. But X now is not much concentrated around $E[X]$. To obtain an exponential high probability, we have to repeat the experience $\Omega(n)$ times. If we want only $\tfrac{1}{n}$ high probability, we need to repeat it $log n$ times. So, the sum of $n$ indepemdent but not identical geometric r.v. is not concentrated around $\alpha\cdot E[x]$, where $\alpha=const$.