Fixed-Time Stable Gradient Flows: Applications to Continuous-Time Optimization

Continuous-time optimization is currently an active field of research in theory; prior work this area has yielded useful insights and elegant methods for proving stability convergence properties the continuous-time algorithms. This article proposes novel gradient-flow schemes that yield to optimal point a convex problem within fixed time from any given initial condition unconstrained optimization, constrained min-max problems. It shown solution modified dynamics exists unique under certain regularity conditions on objective function, while fixed-time via Lyapunov-based analysis. The application gradient flow problems studied assumption dominance, relaxation strong convexity. Then, Newton's method presented exhibits some mild function. Building upon method, technique solving with linear equality constraints yields developed. Finally, general considered, saddle-point obtain