Exploiting Structural Information in Algorithm Designs for Large-Scale Nonlinear Optimization
Abstract
The primary objective of this research is to design efficient first-order algorithms for large-scale nonlinear optimization by exploiting problem structures, and to pursue their applications in data analysis. The last few years have seen an increasing interest in the design of first-order algorithms for solving large-scale nonlinear optimization problems arising from data analysis. In contrast to second-order methods that require Hessian information and induce high computational cost on Hessian matrix inversion, first-order methods rely mostly on matrix-vector multiplications and thus need less computational resources. These methods are more favorable for data analysis applications, especially for the problems that only require solutions with moderate accuracy. In spite of much recent research efforts that have been devoted to first-order algorithms, existing first-order methods are inadequate in dealing with more and more complex optimization problems arising from data analysis. This research focuses on the following two fundamental problems in the design and analysis of first-order methods for data analysis: i) does there exist an algorithm thatutilizes both the structural information of the objective function and feasible set; and ii) is there any problem structure that we can exploit to design algorithms that could avoid expensive traverse of full datasets. If successful, this research will result a new set of efficient optimization methods, including operator sliding methods and accelerated randomized gradient methods, for solving constrained convex or nonconvex problems. It is expected that these methods can judiciously skip expensive operations but still maintain the best possible performance guarantees. This research will further explore the applications of these algorithms for solving a variety of Radar imaging problems that are directly relevant to Navy~s operations and mission. -
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 17, 2020
- Source ID
- N000142012089
Entities
People
- Yuyuan Ouyang
Organizations
- Clemson University
- Office of Naval Research
- United States Navy