Deflation for semismooth equations

Author: 

Farrell, P
Croci, M
Surowiec, T

Publication Date: 

16 May 2019

Journal: 

Optimization Methods and Software

Last Updated: 

2021-11-28T11:19:51.493+00:00

Issue: 

6

Volume: 

35

DOI: 

10.1080/10556788.2019.1613655

page: 

1248-1271

abstract: 

Variational inequalities can in general support distinct solutions. In this paper we study an algorithm for computing distinct solutions of a variational inequality, without varying the initial guess supplied to the solver. The central idea is the combination of a semismooth Newton method with a deflation operator that eliminates known solutions from consideration. Given one root of a semismooth resid- ual, deflation constructs a new problem for which a semismooth Newton method will not converge to the known root, even from the same initial guess. This enables the discovery of other roots. We prove the effectiveness of the deflation technique under the same assumptions that guarantee locally superlinear convergence of a semismooth Newton method. We demonstrate its utility on various finite- and infinite-dimensional examples drawn from constrained optimization, game theory, economics and solid mechanics.

Symplectic id: 

993638

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article