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On Complexity of Deterministic Model Based Derivative Free Optimization MethodsIn many applications of mathematical optimization, one may wish to optimize an objective function without access to its derivatives. These situations call for derivative-free optimization (DFO) methods. Among the most successful approaches in practice are model-based trust-region methods, such as those pioneered by M.J.D Powell. While relatively complex to implement, these methods are now available in standard scientific computing platforms, including MATLAB and SciPy. However, theoretical analysis of their computational complexity lags behind practice. In particular, it is important to bound the number of function evaluations required to achieve a desired level of accuracy. In this lecture we will discuss a variety of derivative free optimization methods and their worst case complexity bounds. We will then show how to systematically derive complexity bounds for classical model based trust region methods and their modern variations. We establish, for the first time, that these methods can have the same worst case complexity than any other known DFO method. We will conclude with some of the open problems and future directions in this domain.Uploaded 06-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices
