Work

A nonsmooth primal-dual method with interwoven PDE constraint solver

Year: 2024

Type: article

Abstract: We introduce an efficient first-order primal-dual method for the solution of nonsmooth PDE-constrained optimization problems. We achieve this efficiency through not solving the PDE or its linearisation on each iteration of the optimization method. Instead, we run the method interwoven with a simple conventional linear system solver (Jacobi, Gauss–Seidel, conjugate gradients), always taking only one step of the linear system solver for each step of the optimization method. The control parameter is updated on each iteration as determined by the optimization method. We prove linear convergence under a second-order growth condition, and numerically demonstrate the performance on a variety of PDEs related to inverse problems involving boundary measurements.

Source: Computational Optimization and Applications

DOI: 10.1007/s10589-024-00587-3

Authors: Bjørn Jensen, Tuomo Valkonen

Institutions: University of Jyväskylä, University of Helsinki, National Polytechnic School

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Helsingin Yliopisto, Helsingin ja Uudenmaan Sairaanhoitopiiri, Academy of Finland, Luonnontieteiden ja Tekniikan Tutkimuksen Toimikunta