An inexact semismooth Newton method with application to adaptive randomized sketching for dynamic optimization

Alshehri, Mohammed; Antil, Harbir; Herberg, Evelyn; Kouri, Drew P.

doi:10.1016/j.finel.2023.104052

An inexact semismooth Newton method with application to adaptive randomized sketching for dynamic optimization

Journal Article · Wed Oct 18 00:00:00 EDT 2023 · Finite Elements in Analysis and Design

DOI:https://doi.org/10.1016/j.finel.2023.104052· OSTI ID:2311364

Alshehri, Mohammed ^[1]; ^[1]; Herberg, Evelyn ^[2]; Kouri, Drew P. ^[3]

George Mason Univ., Fairfax, VA (United States)
Ruprecht-Karls-University, Heidelberg (Germany)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

In many applications, one can only access the inexact gradients and inexact hessian times vector products. Thus it is essential to consider algorithms that can handle such inexact quantities with a guaranteed convergence to solution. An inexact adaptive and provably convergent semismooth Newton method is considered to solve constrained optimization problems. In particular, dynamic optimization problems, which are known to be highly expensive, are the focus. A memory efficient semismooth Newton algorithm is introduced for these problems. The source of efficiency and inexactness is the randomized matrix sketching. Further, applications to optimization problems constrained by partial differential equations are also considered.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Air Force Office of Scientific Research (AFOSR)

Grant/Contract Number:: NA0003525

OSTI ID:: 2311364

Report Number(s):: SAND--2023-14004J

Journal Information:: Finite Elements in Analysis and Design, Journal Name: Finite Elements in Analysis and Design Vol. 228; ISSN 0168-874X

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (24)

Inexact Trust-Region Methods for PDE-Constrained Optimization Kouri, Drew P.; Ridzal, Denis Frontiers in PDE-Constrained Optimization https://doi.org/10.1007/978-1-4939-8636-1_3	book	January 2018
Domain decomposition and model reduction for the numerical solution of PDE constrained optimization problems with localized optimization variables Antil, Harbir; Heinkenschloss, Matthias; Hoppe, Ronald H. W. Computing and Visualization in Science, Vol. 13, Issue 6 https://doi.org/10.1007/s00791-010-0142-4	journal	August 2010
A Variational Discretization Concept in Control Constrained Optimization: The Linear-Quadratic Case Hinze, M. Computational Optimization and Applications, Vol. 30, Issue 1 https://doi.org/10.1007/s10589-005-4559-5	journal	January 2005
Lossy compression for PDE-constrained optimization: adaptive error control Götschel, Sebastian; Weiser, Martin Computational Optimization and Applications, Vol. 62, Issue 1 https://doi.org/10.1007/s10589-014-9712-6	journal	November 2014
Controlling the Kelvin force: basic strategies and applications to magnetic drug targeting Antil, Harbir; Nochetto, Ricardo H.; Venegas, Pablo Optimization and Engineering, Vol. 19, Issue 3 https://doi.org/10.1007/s11081-018-9392-7	journal	June 2018
Approximation numbers=singular values Bennewitz, Christer Journal of Computational and Applied Mathematics, Vol. 208, Issue 1 https://doi.org/10.1016/j.cam.2006.10.042	journal	November 2007
A deterministic pathogen transmission model based on high-fidelity physics Löhner, Rainald; Antil, Harbir; Gimenez, Juan Marcelo Computer Methods in Applied Mechanics and Engineering, Vol. 401 https://doi.org/10.1016/j.cma.2022.114929	journal	November 2022
An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations Barrault, Maxime; Maday, Yvon; Nguyen, Ngoc Cuong Comptes Rendus Mathematique, Vol. 339, Issue 9 https://doi.org/10.1016/j.crma.2004.08.006	journal	November 2004
Real-time observation of vortex lattices in a superconductor by electron microscopy Harada, K.; Matsuda, T.; Bonevich, J. Nature, Vol. 360, Issue 6399 https://doi.org/10.1038/360051a0	journal	November 1992
Domain decomposition and balanced truncation model reduction for shape optimization of the Stokes system Antil, H.; Heinkenschloss, M.; Hoppe, R. H. W. Optimization Methods and Software, Vol. 26, Issue 4-5 https://doi.org/10.1080/10556781003767904	journal	October 2011
Reduced Basis Method for Optimal Control of Unsteady Viscous Flows Ito, K.; Ravindran, S. S. International Journal of Computational Fluid Dynamics, Vol. 15, Issue 2 https://doi.org/10.1080/10618560108970021	journal	October 2001
Using sparse control methods to identify sources in linear diffusion-convection equations Casas, E.; Kunisch, K. Inverse Problems, Vol. 35, Issue 11 https://doi.org/10.1088/1361-6420/ab331c	journal	October 2019
A characterization of superlinear convergence and its application to quasi-Newton methods Dennis, J. E.; Mor{é, Jorge J. Mathematics of Computation, Vol. 28, Issue 126 https://doi.org/10.1090/S0025-5718-1974-0343581-1	journal	May 1974
Minimal Repetition Dynamic Checkpointing Algorithm for Unsteady Adjoint Calculation Wang, Qiqi; Moin, Parviz; Iaccarino, Gianluca SIAM Journal on Scientific Computing, Vol. 31, Issue 4 https://doi.org/10.1137/080727890	journal	January 2009
New Algorithms for Optimal Online Checkpointing Stumm, Philipp; Walther, Andrea SIAM Journal on Scientific Computing, Vol. 32, Issue 2 https://doi.org/10.1137/080742439	journal	January 2010
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems Saad, Youcef; Schultz, Martin H. SIAM Journal on Scientific and Statistical Computing, Vol. 7, Issue 3 https://doi.org/10.1137/0907058	journal	July 1986
Nonlinear Model Reduction via Discrete Empirical Interpolation Chaturantabut, Saifon; Sorensen, Danny C. SIAM Journal on Scientific Computing, Vol. 32, Issue 5 https://doi.org/10.1137/090766498	journal	January 2010
Generalizations of the Dennis--Moré Theorem Dontchev, Asen L. SIAM Journal on Optimization, Vol. 22, Issue 3 https://doi.org/10.1137/110833567	journal	January 2012
Practical Sketching Algorithms for Low-Rank Matrix Approximation Tropp, Joel A.; Yurtsever, Alp; Udell, Madeleine SIAM Journal on Matrix Analysis and Applications, Vol. 38, Issue 4 https://doi.org/10.1137/17M1111590	journal	January 2017
Streaming Low-Rank Matrix Approximation with an Application to Scientific Simulation Tropp, Joel A.; Yurtsever, Alp; Udell, Madeleine SIAM Journal on Scientific Computing, Vol. 41, Issue 4 https://doi.org/10.1137/18M1201068	journal	January 2019
An Efficient, Globally Convergent Method for Optimization Under Uncertainty Using Adaptive Model Reduction and Sparse Grids Zahr, Matthew J.; Carlberg, Kevin T.; Kouri, Drew P. SIAM/ASA Journal on Uncertainty Quantification, Vol. 7, Issue 3 https://doi.org/10.1137/18M1220996	journal	January 2019
Randomized Sketching Algorithms for Low-Memory Dynamic Optimization Muthukumar, Ramchandran; Kouri, Drew P.; Udell, Madeleine SIAM Journal on Optimization, Vol. 31, Issue 2 https://doi.org/10.1137/19M1272561	journal	January 2021
Algorithm 799: revolve: an implementation of checkpointing for the reverse or adjoint mode of computational differentiation Griewank, Andreas; Walther, Andrea ACM Transactions on Mathematical Software, Vol. 26, Issue 1 https://doi.org/10.1145/347837.347846	journal	March 2000
Maximal discrete sparsity in parabolic optimal control with measures Herberg, Evelyn; Hinze, Michael Mathematical Control & Related Fields, Vol. 10, Issue 4 https://doi.org/10.3934/mcrf.2020018	journal	January 2020

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97 MATHEMATICS AND COMPUTING
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An inexact semismooth Newton method with application to adaptive randomized sketching for dynamic optimization

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