An output-sensitive algorithm for multi-parametric LCPs with sufficient matrices
Abstract
This paper considers the multi-parametric linear complementarity problem (pLCP) with sufficient matrices. The main result is an algorithm to find a polyhedral decomposition of the set of feasible parameters and to construct a piecewise affine function that maps each feasible parameter to a solution of the associated LCP in such a way that the function is affine over each cell of the decomposition. The algorithm is output-sensive in the sense that its time complexity is polynomial in the size of the input and linear in the size of the output, when the problem is non-degenerate. We give a lexicographic perturbation technique to resolve degeneracy as well. Unlike for the non-parametric case, the resolution turns out to be nontrivial, and in particular, it involves linear programming (LP) duality and multi-objective LP.
Cite
@article{arxiv.0807.2318,
title = {An output-sensitive algorithm for multi-parametric LCPs with sufficient matrices},
author = {Sebastiano Columbano and Komei Fukuda and Colin Jones},
journal= {arXiv preprint arXiv:0807.2318},
year = {2008}
}