Randomized smoothing for near-convex functions in context of image processing

In this paper the problem of optimization of near-convex functions which can be represented as a sum of strongly convex and bounded functions is addressed. We have noted that in several optimization problems in area of image processing cost functions follow this model. Here we present an algorithm how to minimize such functions using randomized smoothing technique. The technique is an attractive theoretical justification of global optimization properties of SPSA-like algorithms. We present bounds on estimates error after finite number of steps, asymptotic bounds, bounds on estimates' variance and show how the algorithm presented can robustly optimize a function with many similar local minima.