Dynamics of the Douglas-Rachford Method for Ellipses and p-Spheres
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Publication:6278578
DOI10.1007/S11228-017-0457-0arXiv1610.03975MaRDI QIDQ6278578
Brailey Sims, Jonathan M. Borwein, Matthew P. Skerritt, Scott B. Lindstrom, Anna Schneider
Publication date: 13 October 2016
Abstract: We expand upon previous work that examined behavior of the iterated Douglas-Rachford method for a line and a circle by considering two generalizations: that of a line and an ellipse and that of a line together with a -sphere. With computer assistance we discover a beautiful geometry that illustrates phenomena which may affect the behavior of the iterates by slowing or inhibiting convergence for feasible cases. We prove local convergence near feasible points, and---seeking a better understanding of the behavior---we employ parallelization in order to study behavior graphically. Motivated by the computer-assisted discoveries, we prove a result about behavior of the method in infeasible cases.
Nonconvex programming, global optimization (90C26) Nonlinear operators and their properties (47H99) Numerical aspects of recurrence relations (65Q30)
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