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.

contact: ltuncel@math.uwaterloo.ca