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23
votes
5answers
4k views

How to find a closest integer point to intersection of two lines?

Hello. Here's a question that originates from StackOverflow (and the SO crowd isn't really qualified to solve it). We're given two lines on the plane, each of them has at least two integer points ...
5
votes
3answers
2k views

Random Sampling a linearly constrained region in n-dimensions…

Hi, So here is my problem: Given a nonlinear, discontinous, cost function $f(x_1,x_2,..,x_N)$ along with linear constraints $x_n \ge 0, \forall n$ $x_n \le c_n$ and $\sum_{n=1}^N x_n = 1$ find an ...
1
vote
1answer
266 views

Finding a point farthest away from $k$ points in a polygon

There are $k$ points placed inside a polygon and I am interested in finding a point inside the polygon (not necessarily on its boundary) who's minimum distance to any of the $k$ points is maximized. ...
1
vote
1answer
2k views

Detection of Redundant Constraints

Suppose I pose the following query to a constraint logic programming system: ?- Y <= 6 - X, Y <= (- 4) + 4 * X, Y <= 4 + X / 3. Are there systems that would recognize the last inequality as ...
0
votes
1answer
103 views

Linear programming with exponentially many constraints and variables [closed]

From class, I learnt that problems like traveller salesman have a Linear programming representation with exponentially many constraints. Using method of separation, this problem is solved rather ...
4
votes
2answers
398 views

Simplified knapsack problem

There is a problem that I can not solve. Given a set of items (each item has some integer weight) we have to fill bag with some number of copies of these items, with the only restriction that the ...
4
votes
2answers
210 views

point in polytope

Suppose I have the convex hull $P$ of a finite collection of points in $\mathbb{R}^d,$ and I want to see whether a point $p$ is contained in $P.$ This is a standard (some would say the standard linear ...
2
votes
1answer
98 views

optimization of inverse matrix with constraint on matrix elements

everyone! I have this optimization problem with constraint. D and T are symmetric matrice, where T is known and D is the unknown parameter. x and v are two known p-dimensional vectors. The objective ...
2
votes
1answer
106 views

Design constraint systems over the reals

This question is inspired by the discussion at this problem. Suppose I have a design consisting of a finite point set $U$ of size $|U|=m_{\emptyset}$ and a family of $n$ subsets (sometimes called ...