The Differential Inclusion Modeling FISTA Algorithm and Optimality of Convergence Rate in the Case b $\leq3$
The Differential Inclusion Modeling FISTA Algorithm and Optimality of Convergence Rate in the Case b $\leq3$
In this paper we are interested in the differential inclusion $0\in \ddot{x}(t)+\frac{b}{t}\dot{x}(t)+\partial F(x(t))$ in a finite-dimensional Hilbert space $\mathbb{R}^{d}$, where $F$ is a proper, convex, lower semicontinuous function. The motivation of this study is that the differential inclusion models the FISTA algorithm as considered in [A. Chambolle and C. Dossal, …