| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | May 31, 2023 |
| Latest Amendment Date: | May 31, 2023 |
| Award Number: | 2309549 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Jodi Mead
jmead@nsf.gov (703)292-7212 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | July 15, 2023 |
| End Date: | June 30, 2026 (Estimated) |
| Total Intended Award Amount: | $236,770.00 |
| Total Awarded Amount to Date: | $236,770.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
202 HIMES HALL BATON ROUGE LA US 70803-0001 (225)578-2760 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
202 HIMES HALL BATON ROUGE LA US 70803-0001 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | COMPUTATIONAL MATHEMATICS |
| Primary Program Source: |
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| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
Large-scale nonconvex sparse nonlinear optimization problems frequently arise in many modern applications where speed, stability and solution accuracy are critically important. Such applications include optimal control, image processing and stochastic learning. This project improves the implementation and theory of current active set methods for solving large-scale nonlinear optimization problems. Innovation in the project will help to understand the convergence rate and computational complexities of active set methods which have not been fully addressed in the literature. The algorithms and software developed in the project will not only benefit the research in computational optimization but also the investigations of new methods in broader areas of computational science. All the graduate and undergraduate students supported by this project will have opportunities to perform interdisciplinary research in both computational mathematics and data science.
Although interior point methods successfully solve optimization problems with excellent computational complexity, there are rarely global computational complexity results of active set methods for constrained optimization. This project develops practical, efficient and robust active set algorithms and software to solve the large-scale sparse optimization problems to high accuracy with both local fast convergence and global computational complexity guaranteed. In particular, by exploring the affine-scaling techniques and the second-order information the developed methods will have accelerated asymptotic convergence speed, guaranteed global iteration complexity and converge to a (weak) second-order stationary point. In addition, by combining the approach with a generalized minimum eigenvalue procedure and a conjugate gradient method with negative curvature line search, the developed algorithm is expected to have excellent practical performance. All the algorithms will be developed carefully from both theoretical and implementation perspectives to ensure the eventual success of implemented software.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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