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2
votes
3answers
483 views

A simple infinite dimensional optimization problem

I'd be grateful for a reference for the following result, which I believe to be true, and should be well-known. Let the continuous functions $f_0,f_1,\cdots,f_n: [0,1]\rightarrow [0,\infty)$ be ...
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 ...
1
vote
0answers
1k views

Covariance matrix formula interpretation - what am I missing?

I'm reading a paper that outlines the calculation of a covariance matrix like the following: $C=\displaystyle\sum^{N_b}_{i=1}\vec{x}_i\vec{x}_i^T$ What is the order of this matrix? My interpretation ...
1
vote
4answers
2k views

Linear programming piecewise linear objective

I am fairly new at linear programming/optimization and am currently working on implementing a linear program that is stated like this: max $\sum_{i=1}^{k}{p(\vec \alpha \cdot \vec c_i)}$ $s.t. $ ...
10
votes
1answer
1k views

Sum of difference moduli vs. sum of modulus differences

This is a failed attempt of mine at creating a contest problem; the failure is in the fact that I wasn't able to solve it myself. Let $x_1$, $x_2$, ..., $x_n$ be $n$ reals. For any integer $k$, ...
11
votes
3answers
669 views

Deciding membership in a convex hull

Problem: Given points $u,v_1,\dots,v_n\in\mathbb{R}^m$, decide if $u$ is contained in the convex hull of $v_1,\dots,v_n.$ This can be done efficiently by linear programming (time polynomial in ...