Berk U.

Cambridge, MA

berkustun.com

Age: 27

I am a Ph.D. student in the Electrical Engineering and Computer Science Department at MIT. I am interested in developing new methods for data-driven decision-making and using them to solve problems in areas such as climate change, crime prediction, healthcare and revenue management.

4m
revised "Most Similar Vector Problem" on an Integer Lattice?
deleted 5 characters in body
57m
comment How to exclude all points adjacent to a given point from the feasible region of IP
@D.W. Actually, you could also remove $y$ from the feasible region. I will reword. When I first wrote the question, I thought that it wasn't a good idea since $y$ might be the optimal solution so the IP would return a different result. That said, we could solve the IP without $\mathcal{A}(y)$ and $y$. In this case, we would know that the solution we obtain is optimal iff it attains an objective that is less than or equal to $c^Ty$.
1h
comment How to exclude all points adjacent to a given point from the feasible region of IP
@D.W. Thanks for the follow up questions! In terms of motivation, I have a procedure that I can use that will return a "locally optimal" solution $y$. The purpose of removing the adjacent points in $\mathcal{A}(y)$ is to reduce the size of the feasible region and improve the lower bound to the objective value that will be produced by a continuous relaxation. I understand that it may require new variables / constraints, but I was looking for a way to do it using as few variables / constraints as possible.
2h
revised "Most Similar Vector Problem" on an Integer Lattice?
added 17 characters in body
17h
revised "Most Similar Vector Problem" on an Integer Lattice?
edited tags
19h
comment "Most Similar Vector Problem" on an Integer Lattice?
Thank you! Unfortunately the problem is not the same. This paper is trying to find a point on the integer lattice $w \in L$ that minimizes the distance between $\|u-w\|$ as opposed to the point that minimizes the angle between $u$ and $w$.
19h
asked How to exclude all points adjacent to a given point from the feasible region of IP
23h
revised "Most Similar Vector Problem" on an Integer Lattice?
deleted 27 characters in body
1d
revised "Most Similar Vector Problem" on an Integer Lattice?
added 8 characters in body
1d
revised Resource Request for a "Most Similar Vector Problem" on an Integer Lattice?
added 2 characters in body
1d
revised "Most Similar Vector Problem" on an Integer Lattice?
added 71 characters in body
1d
asked "Most Similar Vector Problem" on an Integer Lattice?
1d
asked Resource Request for a "Most Similar Vector Problem" on an Integer Lattice?
1d
revised Are the stationary points of a strongly convex function unique in each dimension?
exposition
1d
accepted Are the stationary points of a strongly convex function unique in each dimension?
1d
comment Are the stationary points of a strongly convex function unique in each dimension?
@StevenTaschuk No just for 1 value of $i \in {1,\ldots,n}$ but not the others.
1d
comment Are the stationary points of a strongly convex function unique in each dimension?
Doesn't work. In 2 dimensions, $\nabla f(x) = x_1^2 + x_2^2$ so $x^* = (0,0)$. At $y = (0,1)$, you do have that $e_1^T \nabla f(y) = 2y_1 = 0$. However, in this case, $y_1=x_1^*$. That being said, your answer was insightful! I think that if the function is $f$ is separable in each dimension, then the property I describe will hold.
1d
asked Are the stationary points of a strongly convex function unique in each dimension?
Jul
24
awarded Notable Question
Jul
23
awarded Yearling
1 2 3 4 5