Complexity of Integer Programming in Reverse Convex Sets via Boundary Hyperplane Cover
Optimization and Control
2024-09-10 v1
Abstract
We study the complexity of identifying the integer feasibility of reverse convex sets. We present various settings where the complexity can be either NP-Hard or efficiently solvable when the dimension is fixed. Of particular interest is the case of bounded reverse convex constraints with a polyhedral domain. We introduce a structure, \emph{Boundary Hyperplane Cover}, that permits this problem to be solved in polynomial time in fixed dimension provided the number of nonlinear reverse convex sets is fixed.
Cite
@article{arxiv.2409.05308,
title = {Complexity of Integer Programming in Reverse Convex Sets via Boundary Hyperplane Cover},
author = {Robert Hildebrand and Adrian Göß},
journal= {arXiv preprint arXiv:2409.05308},
year = {2024}
}