Algorithm Design for Time-Varying Optimization via Nonlinear Control Theory with Applications to Dynamical Systems and Machine Learning
Abstract
Convex optimization theory has long played a major role in engineering (and in particular for the design, analysis and control of dynamical systems), but recent advances in artificial intelligence barely rely on convex optimization and directly work on highly non-convex problems. However, such frameworks only apply to static systems, while many real-world problems have some underlying dynamics. To address this issue, this proposal aims to study timevarying optimization defined as a sequence of non-convex optimization problems that evolve over time. Time-varying optimization has a wide range of applications in sequential decision-making problems, model predictive control, optimal control, reinforcement learning, data-driven - online optimization, and dynamic learning, among others. The solutions of time-varying optimization are trajectories as opposed to points for classic (time-invariant) optimization. In many applications, it is essential to find the best solution of a time-varying optimization problem, referred to as globally minimum solution trajectory. However, the existing local search methods may only find a solution trajectory that satisfies the necessary optimality conditions but is not globally optimal, which we call spurious trajectory.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 07, 2023
- Source ID
- FA95502110250
Entities
People
- Javad Lavaei
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of California Regents