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\begin{abstract}

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.
\end{abstract}


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\section{Acknowledgements}
This work was funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2075 -390740016


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