Lyapunov–function-based framework for smooth strongly convex strongly concave min–max optimization algorithms

We propose a Lyapunov-function–based framework for designing algorithms in min–max optimiza- tion. While Lyapunov functions are traditionally used for convergence analysis, we show that they can also be used as a principled approach for algorithm design. Using this design framework, we demonstrate that it is possible to derive novel algorithms that are convergent by design for smooth and strongly convex strongly concave minmax problems.