具有充分矩阵的多参数线性互补问题的输出敏感算法
An output-sensitive algorithm for multi-parametric LCPs with sufficient matrices
摘要：
研究了具有充分矩阵的多参数线性互补性问题。的主要结果是一个算法，找到一个多面体分解的一组可行的参数，并构造一个分段仿射函数，每个可行的参数映射到一个解决方案的相关LCP在这样一种方式，该功能是仿射在每个细胞的分解。该算法是输出敏感的，在这个意义上，它的时间复杂度是多项式的大小的输入和线性的大小的输出，当问题是非退化的。我们也给出了一个字典序微扰技术来解决简并问题。与非参数情况不同，该解决方案是非平凡的，特别是，它涉及线性规划（LP）的对偶和多目标LP。
英文摘要：
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.
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