Abstract
Given a continuous P 0-function on R n, 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.
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Sznajder, R., Gowda, M.S. (1998). On the Limiting Behavior of the Trajectory of Regularized Solutions of a P0-Complementarity Problem. In: Fukushima, M., Qi, L. (eds) Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods. Applied Optimization, vol 22. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6388-1_19
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DOI: https://doi.org/10.1007/978-1-4757-6388-1_19
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