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5 votes
1 answer
176 views

Efficient counting of integer solutions to linear system

In my research, I have a particular 18x18 matrix $\mathbf{A}$ which defines the linear system $\mathbf{A}\cdot \mathbf{x} \leq \mathbf{-1}$ over the nonnegative integers. And I'm interested in ...
user326210's user avatar
1 vote
1 answer
106 views

Iterated optimal transport

Suppose we are interested in two consecutive transport plans (in the Kantorovich formulation). That is, we are given finite sets $X$, $Y$ and $Z$, endowed with probability measures $\mu_X$, $\mu_Y$ ...
tex.support's user avatar
1 vote
1 answer
169 views

Best projection on non-convex discrete set with two constraints

I want to compute the projection of a vector $\left( x\right) _{1\leq i,j\leq n}\in \lbrack 0,1]^{n\times n}$ on the following discrete set $$ S=\left\{ x\in \{0,1\}^{n\times n}:x_{i,j}+x_{j,i}\leq 1;\...
Goga's user avatar
  • 47
1 vote
0 answers
29 views

Integral hull of a polyhedron Q is polyhedron

Let $Q \subseteq R^n$ be a rational polyhedron and let $Q_I=Convexhull(Q \cap Z^n)$. By finite basis theorem, we have $Q=P+C$ for some rational polytope $P$ and finitely generated cone $C$ where $C=R_+...
Sowbarnika R's user avatar
1 vote
1 answer
73 views

minimize number of unique elements in a vector

I was wondering if there is a simple or known way to minimize the number of unique elements in a decision variable (vector). Note that I'm not asking for minimization of nonzero elements (rank ...
Lorenzo's user avatar
  • 13
1 vote
0 answers
55 views

Separation on discrete set

Consider the set $L = \prod_{i=1}^n\{1,0\}$, i.e. L consists of the element of n-tuples whose entries are 0 or 1. Also we can regard $L$ as a subset of $R^n$. Define linear functions $f(x)= a_1x_1+ \...
user91646's user avatar
1 vote
0 answers
171 views

Finding all feasible solutions

Let $u$ be a $n_{max} \times m$ matrix. Let $z$ be a $n_{max} \times s_{max} \times n_{max}$ cube. Let $w$ be a $n_{max} \times 1$ vector. All the three matrices can have values from the set $\{ 0, 1\}...
ubaabd's user avatar
  • 175
0 votes
1 answer
204 views

Is the linear production game a convex game?

In cooperative game theory, the linear production game (LPG) is defined by letting the characteristic function have the form of a linear programming problem. Does anyone know if the LPG is a convex ...
philipvn's user avatar