Research Interest

Inertial Algorithms for Non-smooth Non-convex Optimization


The inertial algorithms that we study are motivated from physics, namely from a dynamical system that describes the behaviour of a ball that is rolling down a surface subject to friction (also known as heavy-ball dynamical system). The motion of the ball accelerates due to inertia. In analogy to that, the considered algorithms generate a sequence of points that accelerates when it moves in the same direction as before. A classic method for smooth unconstrained optimization problems is the Heavy-ball method. It was introduced by Polyak in 1964 in a paper with the title “Some methods of speeding up the convergence of iteration methods” [Polyak64], which suggests an improved performance of inertial algorithms. The global convergence of the Heavy-ball method for non-convex problems was studied by Zavriev and Kostyuk [ZK93]. For the mechanical interpretation, we refer to [AGR00].