Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Oertel, Timm"'
Given an integer or a non-negative integer solution $x$ to a system $Ax = b$, where the number of non-zero components of $x$ is at most $n$. This paper addresses the following question: How closely can we approximate $b$ with $Ay$, where $y$ is an in
Externí odkaz:
http://arxiv.org/abs/2410.23990
Strict inequalities in mixed-integer linear optimization can cause difficulties in guaranteeing convergence and exactness. Utilizing that optimal vertex solutions follow a lattice structure we propose a rounding rule for strict inequalities that guar
Externí odkaz:
http://arxiv.org/abs/2410.22147
Given a rational pointed $n$-dimensional cone $C$, we study the integer Carath\'{e}odory rank $\operatorname{CR}(C)$ and its asymptotic form $\operatorname{CR^{\rm a}}(C)$, where we consider ``most'' integer vectors in the cone. The main result signi
Externí odkaz:
http://arxiv.org/abs/2211.03150
The Steinitz constant in dimension $d$ is the smallest value $c(d)$ such that for any norm on $\mathbb{R}^{ d}$ and for any finite zero-sum sequence in the unit ball, the sequence can be permuted such that the norm of each partial sum is bounded by $
Externí odkaz:
http://arxiv.org/abs/2201.05874
Autor:
Oertel, Timm1 (AUTHOR), Paat, Joseph2 (AUTHOR) Joseph.paat@sauder.ubc.ca, Weismantel, Robert3 (AUTHOR)
Publikováno v:
Mathematical Programming. Mar2024, Vol. 204 Issue 1/2, p677-702. 26p.
Motivated by problems in optimization we study the sparsity of the solutions to systems of linear Diophantine equations and linear integer programs, i.e., the number of non-zero entries of a solution, which is often referred to as the $\ell_0$-norm.
Externí odkaz:
http://arxiv.org/abs/1912.09763
We consider the asymptotic distribution of the IP sparsity function, which measures the minimal support of optimal IP solutions, and the IP to LP distance function, which measures the distance between optimal IP and LP solutions. We create a framewor
Externí odkaz:
http://arxiv.org/abs/1907.07960
Publikováno v:
In: Lodi A., Nagarajan V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2019. Lecture Notes in Computer Science, vol 11480
We examine how sparse feasible solutions of integer programs are, on average. Average case here means that we fix the constraint matrix and vary the right-hand side vectors. For a problem in standard form with m equations, there exist LP feasible sol
Externí odkaz:
http://arxiv.org/abs/1907.07886
We give an optimal upper bound for the maximum-norm distance from a vertex of a knapsack polyhedron to its nearest feasible lattice point. In a randomised setting, we show that the upper bound can be significantly improved on average. As a corollary,
Externí odkaz:
http://arxiv.org/abs/1805.04592
The support of a vector is the number of nonzero-components. We show that given an integral $m\times n$ matrix $A$, the integer linear optimization problem $\max\left\{\boldsymbol{c}^T\boldsymbol{x} : A\boldsymbol{x} = \boldsymbol{b}, \, \boldsymbol{
Externí odkaz:
http://arxiv.org/abs/1712.08923