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Jul
2
awarded  Curious
Jun
30
comment maximizing a quadratic over linear function
Hi @Rahul, Thank you! It really helps.
Jun
29
revised maximizing a quadratic over linear function
Almost re-write the problem.
Jun
27
revised maximizing a quadratic over linear function
added 13 characters in body
Jun
23
revised maximizing a quadratic over linear function
Explain the details.
Jun
22
asked maximizing a quadratic over linear function
May
22
comment May I know that there is a special structure or solution on this linear fractional optimization?
@mvw. This result is reasonable, since if we take the partial derivative to the objective function, it is non-zero in general, which means the maximum value should be on the boundary. But I don't know whether it is hold in a general $n$, and the result is still all 0 except one $x_i=c$.
May
22
comment May I know that there is a special structure or solution on this linear fractional optimization?
For the case $n=2$, it is shown that the result is always ${x_1=c,x_2=0}$ or ${x_1=0,x_2=c}$.
May
22
revised May I know that there is a special structure or solution on this linear fractional optimization?
edited tags
May
22
comment May I know that there is a special structure or solution on this linear fractional optimization?
Thanks @mvw . Yes, I know that. For the ordinary linear fractional programming, I can follow the method from wiki and reformulate it to the LP. But I want to know whether it will be different for this special form. For example, the analytical solution can be obtained?
May
22
asked May I know that there is a special structure or solution on this linear fractional optimization?
May
18
comment does it have a name : $\prod\left(1-x_i\right)$
Got it. Thanks.
May
18
asked does it have a name : $\prod\left(1-x_i\right)$
Apr
24
comment Inverse of a lower triangular Toeplitz matrix vs. the matrix size
Thanks @Pavel Jiranek. You are so nice. The inverse of the lower triangular Toeplitz matrix has the recursion form, exactly as what you have written. You can have a look at the link: ramanujan.math.trinity.edu/wtrench/research/papers/… But still, I need to think about how to solve it. Thanks.
Apr
24
comment Inverse of a lower triangular Toeplitz matrix vs. the matrix size
Thanks for your clarification. I think your point is $\Vert \mathbf{A}^{-1} \Vert_1 = \mathbf{A}^{-1}e_1 = \sum_{i=0}^{M-1}N^i e_1$. Is it correct? Now the problem is that even I do so, I cannot get clear expression of $N^i$. I hope the expression of $a_i$ could help...
Apr
24
comment Inverse of a lower triangular Toeplitz matrix vs. the matrix size
Hi @Pavel Jiranek, thanks so much for your reply. For the first part of your answer, I can understand, and I have tried before. But I cannot get the result, since the power of $N$ is also complicated. However, I am not clear your last sentence. What is $e_1$ here? What's $N^{-1}e_1$ stands for? I think the inverse of $N$ doesn't exist.
Apr
24
asked Inverse of a lower triangular Toeplitz matrix vs. the matrix size
Oct
27
asked Closed-form Solution of an Integral Equation
Sep
17
awarded  Enthusiast
Aug
28
comment Distribution of the Number of Points in Poisson-Voronoi Tessellation
Hi @Tulip, Thank you for your answer. I have read this paper before, but I remember that in this paper, they didn't justify that $K$ in different cells are independent or not. Have you ever saw some proofs about this? Thanks.