Logarithmic-Barrier Decomposition Interior-Point Methods for Stochastic Linear Optimization in a Hilbert Space

Alzalg, Baha

doi:10.1080/01630563.2019.1709499

Numerical Functional Analysis and Optimization

2020

DOI: 10.1080/01630563.2019.1709499

|View full text |Cite

Logarithmic-Barrier Decomposition Interior-Point Methods for Stochastic Linear Optimization in a Hilbert Space

Baha Alzalg

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Barrier methods based on Jordan–Hilbert algebras for stochastic optimization in spin factors

Alzalg

2024

RAIRO-Oper. Res.

View full text Add to dashboard Cite

Infinite-dimensional stochastic second-order cone programming involves minimizing linear functions over intersections of affine linear manifolds with infinite-dimensional second-order cones. However, even though there is a legitimate necessity to explore these methods in general spaces, there is an absence of infinite-dimensional counterparts for these methods. In this paper, we present decomposition logarithmic-barrier interior-point methods based on unital Jordan-Hilbert algebras for this class of optimization problems in the infinite-dimensional setting. The results show that the iteration complexity of the proposed algorithms is independent on the choice of Hilbert spaces from which the underlying spin factors are formed, and so it coincides with the best-known complexity obtained by such methods for the finite-dimensional setting. We apply our results to an important problem in stochastic control, namely the two-stage stochastic multi-criteria design problem. We show that the corresponding infinite-dimensional system in this case is a matrix differential Ricatti equation plus a finite-dimensional system, and hence, it can be solved efficiently to find the search direction.

show abstract

Barrier methods based on Jordan–Hilbert algebras for stochastic optimization in spin factors

Alzalg

2024

RAIRO-Oper. Res.

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Logarithmic-Barrier Decomposition Interior-Point Methods for Stochastic Linear Optimization in a Hilbert Space

Cited by 1 publication

References 25 publications

Barrier methods based on Jordan–Hilbert algebras for stochastic optimization in spin factors

Barrier methods based on Jordan–Hilbert algebras for stochastic optimization in spin factors

Contact Info

Product

Resources

About