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Convergence of primal-dual solutions for the nonconvex log-barrier method without LICQ. (English) Zbl 1249.90252
Summary: 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 a 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.

90C30 Nonlinear programming
65K10 Numerical optimization and variational techniques
49K40 Sensitivity, stability, well-posedness
49M37 Numerical methods based on nonlinear programming
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