Convergence of successive linear programming algorithms for noisy functions

Christoph Hansknecht (), Christian Kirches () and Paul Manns ()
Additional contact information
Christoph Hansknecht: TU Braunschweig
Christian Kirches: TU Braunschweig
Paul Manns: TU Dortmund University

Computational Optimization and Applications, 2024, vol. 88, issue 2, No 6, 567-601

Abstract: Abstract Gradient-based methods have been highly successful for solving a variety of both unconstrained and constrained nonlinear optimization problems. In real-world applications, such as optimal control or machine learning, the necessary function and derivative information may be corrupted by noise, however. Sun and Nocedal have recently proposed a remedy for smooth unconstrained problems by means of a stabilization of the acceptance criterion for computed iterates, which leads to convergence of the iterates of a trust-region method to a region of criticality (Sun and Nocedal in Math Program 66:1–28, 2023. https://doi.org/10.1007/s10107-023-01941-9 ). We extend their analysis to the successive linear programming algorithm (Byrd et al. in Math Program 100(1):27–48, 2003. https://doi.org/10.1007/s10107-003-0485-4 , SIAM J Optim 16(2):471–489, 2005. https://doi.org/10.1137/S1052623403426532 ) for unconstrained optimization problems with objectives that can be characterized as the composition of a polyhedral function with a smooth function, where the latter and its gradient may be corrupted by noise. This gives the flexibility to cover, for example, (sub)problems arising in image reconstruction or constrained optimization algorithms. We provide computational examples that illustrate the findings and point to possible strategies for practical determination of the stabilization parameter that balances the size of the critical region with a relaxation of the acceptance criterion (or descent property) of the algorithm.

Keywords: Nonsmooth optimization; Global convergence; Noisy optimization (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-024-00564-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:88:y:2024:i:2:d:10.1007_s10589-024-00564-w

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-024-00564-w

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().