Abstract:

The mesh adaptive direct search (MADS) algorithm is designed for constrained black box optimization problems. By black box, we mean that the functions defining the problem are often computed by a long computer code that requires long time to evaluate, and do not guarantee accurate values. We will present MADS together with a hierarchical non-smooth convergence analysis tied to the smoothness of the functions. In the second half of the talk, we will demonstrate the flexibility of MADS by devising a framework to identify locally optimal algorithmic parameters. The framework makes provision for surrogate objectives. Parameters are sought so as to minimize some measure of performance of the algorithm being fine-tuned. This framework is then specializing to the identification of locally optimal trust-region parameters in unconstrained optimization. Each function call requires several hours and may not always return a predictable result. A surrogate function, taylored to the experiment at hand, is used to guide MADS towards a local solution. The parameters thus identified differ from traditionally used values, and are used to solve a problem from the CUTER collection that remained otherwised unsolved in a reasonable time using traditional values.