## High-order large-step interior point algorithms for linear
complementarity problems

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Zhao Gong Yun

In this paper we study a type of high-order large-step interior point
algorithms for solving linear complementarity problems. These algorithms
are implicitly associated with a large neighborhood whose size may
depend on the dimension of the problems. The complexity of these
algorithms depends on the size of the neighborhood. By using high-order
power series (so the name high-order algorithm), the complexity can be
reduced. We will show that the complexity upper bound for high-order
large-step algorithms is asymptotically, as the order tends to infinity,
equal to that for short-step algorithms.
Technical Report No. 650, Department of Mathematics, National University
of Singapore, 0511, SINGAPORE