The Linear Complementarity Problem
Chapter
Abstract
This paper discusses a number of observations and conclusions drawn from ongoing research into more efficient algorithms for solving nonconvex linear complementarity problems (LCP). We apply interior point approaches and partitioning techniques to classes of problems that can be solved efficiently. Using the potential reduction algorithm, we characterize some classes of problems that can be solved in polynomial time. The same algorithm is used for the solution of problems with a row-sufficient matrix. The algorithm also generates a stationary point for the LCP in fully polynomial approximation time. When the problem data has no structure, we show equivalence of mixed integer programming problems and the linear complementarity problems.
Key words
Linear Complementarity Problem NP-hard Integer Programming Interior Point MethodsPreview
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