Differentiable Local Barrier-Penalty Paths [chapter]

C. Grossmann
IFIP International Federation for Information Processing  
Perturbations of Karush-Kuhn-Tuckerconditions play an importantrole forprimaldual interior point methods. Beside the usual logarithmic barrier various further techniques of sequential unconstrained minimization are well known. However other than logarithmic embeddings are rarely studied in connection with Newton path-following methods. A key property that allows to extend the class of methods is the existence of a locally Lipschitz continuous path leading to a primal-dual solution of the
more » ... tem. In this paper a rather general class of barrier/penalty functions is studied. In particular, under LICQ regularity and strict complementarity assumptions the differentiability of the path generated by any choice of barrier/penalty functions from this class is shown. This way equality as well as inequality constraints can be treated direcdy without additional transformations. Further, it will be sketched how local convergence of the related Newton pathfollowing methods can be proved without direct applications of self-concordance properties. keywords: Perturbed KKT-systems, general barrier-penalty embedding, differentiable path, path-following methods, interior point methods 'Paper written with financial support of DFG grant GR 1777/2-2. Please use the following format when citing this chapter:
doi:10.1007/0-387-33882-9_18 dblp:conf/ifip7/Grossmann06 fatcat:m5q3seurdrhzjfpf4rzujlhnk4