joint work with Serge Gratton, Luis Nunes Vicente
In this talk, we describe a technique that separately computes first-and second-order steps, in order to better relate each step to its corresponding stationarity criterion. Such an approach can lead to larger steps and decreases in the objective, which positively impacts both the complexity analysis and the practical behavior. Although its applicability is wider, we present our concept within a trust-region framework without derivatives. This allows us to highlight interesting connections between our decoupling paradigm and the criticality steps used to guarantee convergence of such methods.
joint work with Andrea Cristofari
In this talk, we describe a new approach for minimizing a black-box function over a structured convex set. We analyze the theoretical properties of the method. Furthermore, we report some numerical results showing that the algorithm scales up well when the dimensions of the problems get large.
joint work with Christian Ebenbauer
A novel class of derivative-free optimization algorithms based on non-commutative maps for multi-variable optimization problems is presented. The main idea is to utilize certain non-commutative maps in order to approximate the gradient of the objective function. We show how these maps can be constructed by so-called generating functions incorporated with either single- or two-point objective evaluation polices and how periodic exploration sequences can be designed to approximate gradients. Finally, we analyze the convergence of the proposed class of algorithms and present benchmarking results.