Superlinear Primal-Dual Affine Scaling Algorithms for LCP

We describe an interior-point algorithm for monotone linear complementarity problems in which primal-dual affine scaling is used to generate the search directions. The algorithm is shown to have global and superlinear convergence with Q-order up to (but not including) two. The technique is shown to be consistent with a potential-reduction algorithm, yielding the first potential-reduction algorithm that is both globally and superlinearly convergent. Key words: interior-point methods, primal-dual affine scaling, linear programming, linear complementarity 1 Introduction During the past three years, we have seen the appearance of several papers dealing with primal-dual interior-point algorithms for linear programs (LP) and monotone linear complementarity problems (LCP) that are superlinearly or quadratically convergent. For LP, these works include McShane [7], Mehrotra [8], Tsuchiya [15], Ye [17], Ye et al. [19], Zhang and Tapia [21], and Zhang, Tapia, and Dennis [22]. For LCP, we mentio..