Iterated Linear Optimization
Optimization and Control
2021-03-18 v2 Data Structures and Algorithms
Combinatorics
Abstract
We introduce a fixed point iteration process built on optimization of a linear function over a compact domain. We prove the process always converges to a fixed point and explore the set of fixed points in various convex sets. In particular, we consider elliptopes and derive an algebraic characterization of their fixed points. We show that the attractive fixed points of an elliptope are exactly its vertices. Finally, we discuss how fixed point iteration can be used for rounding the solution of a semidefinite programming relaxation.
Cite
@article{arxiv.2012.02213,
title = {Iterated Linear Optimization},
author = {Pedro Felzenszwalb and Caroline Klivans and Alice Paul},
journal= {arXiv preprint arXiv:2012.02213},
year = {2021}
}