Oblivious Randomized Direct Search for Real-Parameter Optimization

The focus is on black-box optimization of a function f : RN R given as a black box, i. e. an oracle for f-evaluations. This is commonly called direct search, and in fact, most methods for direct search are heuristics. Theoretical results on the performance/behavior of such heuristics are still rare. One reason: Like classical optimization algorithms, also direct-search methods face the challenge of step-size control, and usually, the more sophisticated the step-size control, the harder the analysis. Obviously, when we want the search to actually converge to a stationary point (i. e., the distance from this point tends to zero) at a nearly constant rate, then step sizes must be adapted. In practice, however, obtaining an -approximation for a given > 0 is often sufficient, and usually all N parameters are bounded, so that the maximum distance from the optimum is bounded. Thus, in such cases reasonable step sizes lie in a predetermined bounded interval. Considering the minimization of...

• Type: Conference
• Year: 2008
• Where: ESA
• Authors: Jens Jägersküpper
• Keywords: Algorithms, Direct Search, ESA 2008, Step Sizes, Step-size Control