In the present paper rather general penalty/barrier path-following methods (e.g. with p-th power penalties, logarithmic barriers, SUMT, exponential penalties) applied to linearly constrained convex optimization problems are studied. In particular, unlike in previous studies [1,11], here simultaneously different types of penalty/barrier embeddings are included. Together with the assumed 2nd order sufficient optimality conditions this required a significant change in proving the local existence of some continuously differentiable primal and dual path related to these methods. In contrast to standard penalty/barrier investigations in the considered path-following algorithms only one Newton step is applied to the generated auxiliary problems. As a foundation of convergence analysis the radius of convergence of Newton's method depending on the penalty/barrier parameter is estimated. There are established parameter selection rules which guarantee the overall convergence of the considered path-following penalty/barrier techniques.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1001,
author = {Christian Grossmann},
title = {Penalty/barrier path-following in linearly constrained optimization},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {20},
year = {2000},
pages = {7-26},
zbl = {0980.90085},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1001}
}
Christian Grossmann. Penalty/barrier path-following in linearly constrained optimization. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 20 (2000) pp. 7-26. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1001/
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