On the Limiting Behavior of the Trajectory of Regularized Solutions of a P0-Complementarity Problem

Given a continuous P₀-function on Rn, we consider the nonlinear complementarity problem NCP(f) and the trajectory of regularized solutions {x(ε):0 < ε < ∞} where x(ε) is the unique solution of NCP(f _ε ) with f _ε (x):= f (x) +ε x. Given a sequence {x(ε _k )} with ε _k ↓ 0, we discuss (i) the existence of a bounded/convergent subsequence in the affine case, (ii) a property of any subsequential limit x*, and (iii) the convergence of the entire trajectory in the polynomial case.