Interior point algorithm for nonlinear complementarity problems

In this paper, we propose a new large-update primal–dual interior point algorithm for P ∗ complementarity problems (CPs). Different from most interior point methods which are based on the logarithmic kernel function, the new method is based on a class of kernel functions ψ ( t ) = ( t p + 1 − 1 ) / ( p + 1 ) + ( t − q − 1 ) / q , p ∈ [ 0 , 1 ] , q > 0 . We show that if a strictly feasible starting point is available and the undertaken problem satisfies some conditions, then the new large-update primal–dual interior point algorithm for P ∗ CPs has O ( ( 1 + 2 κ ) n log n log ( n μ 0 / ε ) ) iteration complexity which is currently the best known result for such methods with p = 1 and q = ( log n ) / 2 − 1 .