Distilling common randomness from bipartite quantum states
Igor Devetak, Andreas Winter
ISIT 2003
We consider the global and local convergence properties of a class of Lagrangian barrier methods for solving nonlinear programming problems. In such methods, simple bound constraints may be treated separately from more general constraints. The objective and general constraint functions are combined in a Lagrangian barrier function. A sequence of such functions are approximately minimized within the domain defined by the simple bounds. Global convergence of the sequence of generated iterates to a first-order stationary point for the original problem is established. Furthermore, possible numerical difficulties associated with barrier function methods are avoided as it is shown that a potentially troublesome penalty parameter is bounded away from zero. This paper is a companion to previous work of ours on augmented Lagrangian methods.
Igor Devetak, Andreas Winter
ISIT 2003
Charles A Micchelli
Journal of Approximation Theory
Donald Samuels, Ian Stobert
SPIE Photomask Technology + EUV Lithography 2007
M. Shub, B. Weiss
Ergodic Theory and Dynamical Systems