Finite-Time Optimization via Scaled Gradient-Momentum Flows
This work provides a theoretical framework for achieving finite-time convergence in continuous-time optimization, which is a known bottleneck in optimization theory.
The paper develops a scaled gradient-momentum framework for continuous-time optimization that achieves global finite-time convergence, with explicit conditions linking gradient-dominance and finite-time stability. Numerical experiments validate the theory.
In this paper, we develop a scaled gradient-momentum framework for continuous-time optimization that achieves global finite-time convergence. A state-dependent scaling mechanism is introduced to enable classical dynamics, such as Heavy-Ball-type and proportional-integral (PI)-type flows, to attain finite-time convergence. We establish explicit conditions that bridge the gradient-dominance property of the objective function and finite-time stability of the proposed scaled dynamics. Numerical experiments validate the theoretical results.