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An inexact semismooth Newton method with application to adaptive randomized sketching for dynamic optimization
Abstract
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.
- Authors:
-
[1];
- George Mason Univ., Fairfax, VA (United States)
- Ruprecht-Karls-University, Heidelberg (Germany)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Air Force Office of Scientific Research (AFOSR)
- OSTI Identifier:
- 2311364
- Report Number(s):
- SAND-2023-14004J
Journal ID: ISSN 0168-874X
- Grant/Contract Number:
- NA0003525
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Finite Elements in Analysis and Design
- Additional Journal Information:
- Journal Volume: 228; Journal ID: ISSN 0168-874X
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Nonsmooth optimization; Inexact gradient and Hessian; Semismooth Newton; Adaptivity; Convergence analysis; Compression methods; Randomized sketching; Measure control; Variational discretization
Citation Formats
Alshehri, Mohammed, Antil, Harbir, Herberg, Evelyn, and Kouri, Drew P. An inexact semismooth Newton method with application to adaptive randomized sketching for dynamic optimization. United States: N. p., 2023.
Web. doi:10.1016/j.finel.2023.104052.
Alshehri, Mohammed, Antil, Harbir, Herberg, Evelyn, & Kouri, Drew P. An inexact semismooth Newton method with application to adaptive randomized sketching for dynamic optimization. United States. https://doi.org/10.1016/j.finel.2023.104052
Alshehri, Mohammed, Antil, Harbir, Herberg, Evelyn, and Kouri, Drew P. Wed .
"An inexact semismooth Newton method with application to adaptive randomized sketching for dynamic optimization". United States. https://doi.org/10.1016/j.finel.2023.104052.
@article{osti_2311364,
title = {An inexact semismooth Newton method with application to adaptive randomized sketching for dynamic optimization},
author = {Alshehri, Mohammed and Antil, Harbir and Herberg, Evelyn and Kouri, Drew P.},
abstractNote = {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.},
doi = {10.1016/j.finel.2023.104052},
journal = {Finite Elements in Analysis and Design},
number = ,
volume = 228,
place = {United States},
year = {Wed Oct 18 00:00:00 EDT 2023},
month = {Wed Oct 18 00:00:00 EDT 2023}
}
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