Analysis of Interior-Point Paths.
Infeasible-interior-point paths are the main tools in interior-point methods for solving many kinds of optimization problems. These paths are usually parametrized by a penalty-parameter r ↓ 0 and further parameters describing their off-centrality and infeasiblilty. Starting with an early result of C. Witzgall et al. [12] in linear programming, this paper gives an overview on results concerning the existence of these paths, their analyticity and the limiting behavior of their derivatives as r ↓ 0, and this also for degenerate problems in the areas of linear programming, linear complementarity problems, and semi-definte programming.
Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Germany.
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Stoer
infeasible interior-point paths; linear complementarity problems; linear programs; semidefinite linear complementarity problems; semidefinite linear programs