Reflection methods for inverse problems with application to protein conformation determination

TL;DR

This paper explores the application of the Douglas-Rachford reflection method to protein conformation determination, demonstrating how problem-specific heuristics can enhance its effectiveness in this complex inverse problem.

Contribution

It introduces tailored heuristics for the Douglas-Rachford method that leverage the structure of protein conformation problems within matrix completion.

Findings

Heuristics improve convergence in protein conformation tasks

Method effectively handles the intersection of multiple constraints

Application demonstrates potential for structural biology problems

Abstract

The Douglas-Rachford reflection method is a general purpose algorithm useful for solving the feasibility problem of finding a point in the intersection of finitely many sets. In this chapter we demonstrate that applied to a specific problem, the method can benefit from heuristics specific to said problem which exploit its special structure. In particular, we focus on the problem of protein conformation determination formulated within the framework of matrix completion, as was considered in a recent paper of the present authors.