Interior-Point Abstracts

Primal-dual symmetry and scale invariance of interior-point algorithms for convex optimization

Levent Tuncel

We present a definition of symmetric primal-dual algorithms for convex optimization problems expressed in the conic form. After describing a generalization of the $v-$space approach for such optimization problems, we show that a symmetric $v-$space approach can be developed for a convex optimization problem in the conic form if and only if the underlying cone is homogeneous and self-dual. We provide an alternative definition of self-scaled barriers and then conclude with a discussion of the scalings of the variables which keep the underlying convex cone invariant.

Research Report 96--18, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, November 1996.