Solutions of several problems can be modelled as solutions of nonsmooth equations. Then, Newton-type methods for solving such equations induce particular iteration steps (actions) and regularity requirements in the original problems. We study these actions and requirements for nonlinear complementarity problems (NCP's) and Karush-Kuhn-Tucker systems (KKT) of optimization models. We demonstrate their dependence on the applied Newton techniques and the corresponding reformulations. In this way, connections...
This paper characterizes completely the behavior of the logarithmic barrier method under a standard second order condition, strict (multivalued) complementarity and MFCQ at a local minimizer. We present direct proofs, based on certain key estimates and few well–known facts on linear and parametric programming, in order to verify existence and Lipschitzian convergence of local primal-dual solutions without applying additionally technical tools arising from Newton–techniques.
Studying a critical value function in parametric nonlinear programming, we recall conditions guaranteeing that is a function and derive second order Taylor expansion formulas including second-order terms in the form of certain generalized derivatives of . Several specializations and applications are discussed. These results are understood as supplements to the well–developed theory of first- and second-order directional differentiability of the optimal value function in parametric optimization....
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