Assume we have a set of samples and estimate the underlying distribution with a non-parametric density estimator like the Kernel Density Estimator. Lets assume with a gaussian kernel.
In my case it is highly non-convex and multimodal. My goal is to find this distribution's peak. I would handle this by sampling from the distribution itself. Maybe in combination with a gradient ascent to be sure ending up in local maxima.
What are state of the art methods to find the peak of such a density?