Graph implementations for nonsmooth convex programs. (English) Zbl 1205.90223

Grant, Michael C.; Boyd, Stephen P.

Blondel, Vincent D. (ed.) et al., Recent advances in learning and control. Festschrift for Mathukumalli Vidyasagar on the occasion of his sixtieth birthday. London: Springer (ISBN 978-1-84800-154-1/pbk). Lecture Notes in Control and Information Sciences 371, 95-110 (2008).

Summary: We describe graph implementations, a generic method for representing a convex function via its epigraph described in a disciplined convex programming framework. This simple and natural idea allows a very wide variety of smooth and nonsmooth convex programs to be easily specified and efficiently solved using interiorpoint methods for smooth or cone convex programs.
For the entire collection see [Zbl 1140.93006].

MSC:

90C25

Convex programming

Keywords:

disciplined convex programming; optimization modeling languages; semidefinite programming; second-order cone programming; conic optimization; nondifferentiable functions

Software:

YALMIP; SDPT3; LOQO; CVX; SeDuMi