Robust Time-Varying Continuous-Time Optimization with Pre-Defined Finite-Time Stability

Abstract

In this paper we propose a new family of continuous-time optimization algorithms based on discontinuous second order gradient optimization flows, with finite-time convergence guarantees to local optima, for locally strongly convex time-varying cost functions. To analyze our flows, we first extend a well-know Lyapunov inequality condition for finite-time stability, to the case of time-varying differential inclusions. We then prove the convergence of these second-order flows in finite-time. We show the performance of these flows on a time-varying quadratic cost and on the nonlinear time-varying Rosenbrock function.