Abstract
We present new infeasible path-following methods for linear monotone complementarity problems based on Auslender, Teboulle and Ben-Tiba’s log-quadratic barrier functions. The central paths associated with these barriers are always well defined and, for those problems which have a solution, convergent to a pair of complementary solutions. Starting points in these paths are easy to compute. The theoretical iteration-complexity of these new path-following methods is derived and improved by a strategy which uses relaxed hybrid proximal-extragradient steps to control the quadratic term. Encouraging preliminary numerical experiments are presented.
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