A Replication Study (Romero & Benosman, ICML 2020)
This repository contains a replication and validation of the finite-time convergent optimization flows proposed by Romero & Benosman (ICML 2020). The project was completed as part of the Optimization for Engineers course at Utah State University.
Classical gradient flows converge asymptotically to an optimum. In contrast, the methods studied here achieve exact convergence in finite, bounded time. This project implements and validates both first-order and second-order continuous-time optimization flows, reproducing all experimental figures from the original paper.
- q-Rescaled Gradient Flow (q-RGF)
- Finite-time convergence for gradient-dominated functions when q > p
- Verified theoretical settling-time bounds
- Rescaled Newton Flow (RNF)
- Prescribed convergence time for strongly convex functions
- Uses Hessian information with time-rescaling
- Nesterov-style momentum discretization
- Accelerated backtracking line search
- Comparison against Gradient Descent, Nesterov Accelerated GD, and Newton’s method
- Language: Python
- Numerical integration: SciPy ODE solvers (RK45)
- Libraries: NumPy, SciPy, Matplotlib
- Test functions:
- p-norm function (gradient-dominated)
- Rosenbrock function (strongly convex)
- Log-sum-exp function (high-dimensional convex)
- Successfully reproduced all five figures from Section 5 of the original paper
- Verified finite-time convergence bounds for q-RGF
- Demonstrated prescribed-time convergence behavior for RNF
- Showed that Nesterov-style discretization provides strong practical performance
SRC/– continuous-time optimization flow implementationsfigures/– generated plots (Figures 1–5)docs/– final project report
Romero, O., & Benosman, M. (2020). Finite-Time Convergence in Continuous-Time Optimization. ICML.