Given: I have 2D non-parametric formula that provides instantaneous intensity at certain (x,y) location.
Required: I want to en-circle a region where the density is high via optimization. In other words fitting a circle whose radius must be optimized such that the density is maximum at certain region.
Analogy: Consider an oil spill in water (assume stationary). I want to find an area enclosed inside a circle that constitutes highest density. It is to identify most important spots that require cleaning fast. So less dense area is not cleaned first.
The density can be computed by performing monte-carlo integration of the intensity values inside the a circle (size of which has to be optimized) and then dividing by the area of the circle. So if the size of circle grows so is its area. The outcome of optimization is the value of the radius of the circle and its position.
Question: Now considering the area is huge, and the problem cannot be solved analytically, what are some of the approaches/heuristics that I can use to solve the problem?