  Evolution strategy (ES) is one of promising classes of algorithms for
black-box continuous optimization. Despite its broad successes in applications,
theoretical analysis on the speed of its convergence is limited on convex
quadratic functions and their monotonic transformation. In this study, an upper
bound and a lower bound of the rate of linear convergence of the (1+1)-ES on
locally $L$-strongly convex functions with $U$-Lipschitz continuous gradient
are derived as $\exp\left(-\Omega_{d\to\infty}\left(\frac{L}{d\cdot
U}\right)\right)$ and $\exp\left(-\frac1d\right)$, respectively. Notably, any
prior knowledge on the mathematical properties of the objective function such
as Lipschitz constant is not given to the algorithm, whereas the existing
analyses of derivative-free optimization algorithms require them.
