Partial smoothness and constant rank
Optimization and Control
2018-07-10 v1
Abstract
The idea of partial smoothness in optimization blends certain smooth and nonsmooth properties of feasible regions and objective functions. As a consequence, the standard first-order conditions guarantee that diverse iterative algorithms (and post-optimality analyses) identify active structure or constraints. However, by instead focusing directly on the first-order conditions, the formal concept of partial smoothness simplifies dramatically: in basic differential geometric language, it is just a constant-rank condition. In this view, partial smoothness extends to more general mappings, such as saddlepoint operators underlying primal-dual splitting algorithms.
Cite
@article{arxiv.1807.03134,
title = {Partial smoothness and constant rank},
author = {Adrian S. Lewis and Jingwei Liang},
journal= {arXiv preprint arXiv:1807.03134},
year = {2018}
}