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Minimize RSR Award Detail

Research Spending & Results

Award Detail

Awardee:MIAMI UNIVERSITY
PD/PI:
  • Ebrahim Sarabi
  • sarabim@MiamiOH.edu
Award Date:08/02/2021
Estimated Total Award Amount: $ 194,957
Funds Obligated to Date: $ 194,957
  • FY 2021=$194,957
Start Date:08/15/2021
End Date:07/31/2024
Transaction Type:Grant
Agency:NSF
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:Second-Order Variational Properties of Composite Optimization and Applications
Federal Award ID Number:2108546
DUNS ID:041065129
Parent DUNS ID:041065129
Program:APPLIED MATHEMATICS
Program Officer:
  • Eun Heui Kim
  • (703) 292-2091
  • eukim@nsf.gov

Awardee Location

Street:500 E High Street
City:Oxford
State:OH
ZIP:45056-3653
County:Oxford
Country:US
Awardee Cong. District:08

Primary Place of Performance

Organization Name:Miami University
Street:Bachelor Hall, 211
City:Oxford
State:OH
ZIP:45056-1602
County:Oxford
Country:US
Cong. District:08

Abstract at Time of Award

This project will study the behavior of solutions to optimization problems, which appear in applications such as regression models, sparse approximation of signals, image processing, and sensor location problems. In addition, the principal investigator will design numerical algorithms that can solve the optimization problems efficiently. The investigator will exploit various tools and techniques of variational analysis for these optimization problems with data that may not be differentiable in the usual way, and study applications in numerical algorithms. Graduate students and a postdoctoral researcher will participate in this project. The project investigates second-order variational properties of important classes of composite optimization problems, including piecewise linear-quadratic composite problems and different classes of matrix optimization problems. The proposal has three main objectives. First, the investigator will study parabolic regularity and twice epi-differentiability of the aforementioned classes of optimization problems. In particular, the investigator pays special attention to the augmented Lagrangians associated with composite optimization problems, studies their twice epi-differentiability, and characterizes the quadratic growth condition for this class of functions via the second-order sufficient condition. Second, the investigator will study important stability properties of composite problems, including strong metric regularity, strong metric subregularity, and non-criticality of their Lagrange multipliers. Finally, the investigator will conduct local and global convergence analysis of the augmented Lagrangian method for important classes of composite optimization problems with special emphasis on those optimization problems whose Lagrange multipliers are not unique. In doing so, the investigator mainly relies on the concept of the second subderivative and its recent developments. 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.

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