Scalable First-Order Methods for Large-Scale Optimization- Theory and Computation
Abstract
Linear programming (LP), quadratic programming (QP), and nonlinear convex programming (NLP) are essential tools in computational science and applied mathematics with wide-ranging applications. Current state-of-the-art commercial solvers for these problems rely on active set (simplex) or Newton barrier methods, facing scalability challenges due to the matrix factorization step. The effort seeks to develop next-generation algorithms and software using matrix-free first-order methods (FOMs) that only require matrix-vector multiplications. This enables scalability on modern architectures like GPUs and distributed computing. The project integrates complexity analysis, numerical linear algebra, software development, benchmarking, and modern computing architecture utilization. All proposed algorithms will offer rigorous theoretical guarantees, high-performance implementation, and testing on real-world benchmark problems. The success of the research can significantly scale up and speed up LP, QP, and NLP, impacting downstream applications and reshaping the optimization solver industry. The PI s proven expertise in optimization and solver development instills confidence in successfully executing this research.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 05, 2025
- Source ID
- FA95502410051
Entities
People
- John Birge
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Chicago