Stochastic and Distributed First-Order Methods for Big Convex Optimization
Abstract
Numerous data-driven decision problems arising in a variety of Navy applications, including interdiction, logistics, planning, scheduling, and sequencing, can be solved as a single convex optimization problem or a sequence of such problems generated by convex relaxation techniques. Nowadays, especially in the big data era, these problems are often in big scale and known as big convex optimization (BCO), characterized by objective function and constraints involving a plethora of convex functions. The enormity of BCO transcends the capabilities of existing methods and poses formidable challenges to Navy practitioners. To tackle these challenges, we propose a novel algorithmic framework for both BCO and its distributed variant. This framework is poised to yield innovative algorithmsthat not only possess attractive theoretical performance guarantees but also empower Navy practitioners to solve these problems efficiently. In particular, we will develop stochastic first-order proximal augmented Lagrangian methods for BCO. These approaches leverage a stochastic proximal point paradigm, wherein the subproblems are tactically solved using novel stochastic accelerated proximalgradient methods. Furthermore, we will propose pioneering distributed stochastic first-order proximal augmented Lagrangian methods tailored for distributed BCO, whose subproblems will be efficiently solved via novel distributed stochastic accelerated proximal gradient methods.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Nov 09, 2024
- Source ID
- N000142412702
Entities
People
- Zhaosong Lu
Organizations
- Office of Naval Research
- Regents of the University of Minnesota
- United States Navy