Nonlinear Rescaling in discrete minimax

We present a general Nonlinear Rescaling (NR) methods for discrete minimax problem. The fundamental difference between the NR approach and the smoothing technique consists of using the Lagrange multipliers as the main driving force to improve the convergence rate and the numerical stability. In contrast to the smoothing technique the NR methods converge to the primal-dual solution under a fixed scaling parameter. It allows to avoid the ill-conditioning and at the same time improves the convergence rate. In particular, under the standard second order optimality condition the NR method converges with Q-linear rate when the scaling parameter is fixed, but small enough. Partially supported by NSF Grant DMS-9705672 Partially supported by NASA Grant NAG-1-1929