Accelerated Alternating Minimization and Adaptability to Strong Convexity

Understand

In the first part of the paper we consider accelerated first order optimization method for convex functions with $L$-Lipschitz-continuous gradient, that is able to automatically adapts to problems which satisfies Polyak-{\L}ojasiewicz condition or which is strongly convex with the value of parameter equal to $\mu$.

• In these cases method poses linear convergence with factor $\frac{\mu}{L}$, if $\mu$ is unknown.
• If the problem is strongly convex and $\mu$ is known, than the method possesses linear convergence with the factor $\sqrt{\frac{\mu}{L}}$.
• If that are not the cases, the method converges with a rate $O(1/k^2)$.