4 papers
Optimal Proximity Bound and Product Function Estimates in Integer Linear Programming
Iskander Aliev, Gennadiy Averkov, William Jones +1
We obtain an optimal proximity bound for integer linear programs in standard form max{cx: Ax=b, x nonnegative integer}, where A is an integer mxn matrix of rank m<n and b is an int…
Sparse Approximation in Lattices and Semigroups
Stefan Kuhlmann, Timm Oertel, Robert Weismantel
This paper deals with the following question: Suppose that there exist an integer or a non-negative integer solution to a system , where the number of non-zero componen…
Asymptotic Bounds and Online Algorithms for Average-Case Matrix Discrepancy
Dmitriy Kunisky, Timm Oertel, Nicola Wengiel +1
We study the matrix discrepancy problem in the average-case setting. Given a sequence of symmetric matrices , its discrepancy is defined as the minimal…
Exact Decomposition Branching exploiting Lattice Structures
Katrin Halbig, Timm Oertel, Dieter Weninger
Strict inequalities in mixed-integer linear optimization can cause difficulties in guaranteeing convergence and exactness. Utilizing that optimal vertex solutions follow a lattice…