  This paper considers the problem of designing accelerated gradient-based
algorithms for optimization and saddle-point problems. The class of objective
functions is defined by a generalized sector condition. This class of functions
contains strongly convex functions with Lipschitz gradients but also non-convex
functions, which allows not only to address optimization problems but also
saddle-point problems. The proposed design procedure relies on a suitable class
of Lyapunov functions and on convex semi-definite programming. The proposed
synthesis allows the design of algorithms that reach the performance of
state-of-the-art accelerated gradient methods and beyond.

Optimization and Control;Systems and Control;Systems and Control