New error bound for linear complementarity problem of $ S $-$ SDDS $-$ B $ matrices

<abstract><p>$ S $-$ SDDS $-$ B $ matrices is a subclass of $ P $-matrices which contains $ B $-matrices. New error bound of the linear complementarity problem for $ S $-$ SDDS $-$ B $ matrices is presented, which improves the corresponding result in ^{[<xref ref-type="bibr" rid="b1">1</xref>]}. Numerical examples are given to verify the corresponding results.</p></abstract>

Path-following interior-point algorithm for monotone linear complementarity problems

This paper presents a path-following full-Newton step interior-point algorithm for solving monotone linear complementarity problems. Under new choices of the defaults of the updating barrier parameter [Formula: see text] and the threshold [Formula: see text] which defines the size of the neighborhood of the central-path, we show that the short-step algorithm has the best-known polynomial complexity, namely, [Formula: see text]. Finally, some numerical results are reported to show the efficiency of our algorithm.

Predictor-Corrector Interior-Point Algorithm for the General Linear Complementarity Problem

We study a predictor-corrector interior-point algorithm for solving general linear complementarity problems from the implementation point of view. We analyze the method proposed by Illés, Nagy and Terlaky [1] that extends the algorithm published by Potra and Liu [2] to general linear complementarity problems. A new method for determining the step size of the corrector direction is presented. Using the code implemented in the C++ programming language, we can solve large-scale problems based on sufficient matrices.