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Convergence of primal-dual solutions for the nonconvex log-barrier method without LICQ

Christian Grossmann; Diethard Klatte; Bernd Kummer — 2004

Kybernetika

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.

On second–order Taylor expansion of critical values

Stephan Bütikofer; Diethard Klatte; Bernd Kummer — 2010

Kybernetika

Studying a critical value function $ϕ$ in parametric nonlinear programming, we recall conditions guaranteeing that $ϕ$ is a $C^{1, 1}$ function and derive second order Taylor expansion formulas including second-order terms in the form of certain generalized derivatives of $D ϕ$ . 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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