Charles Audet (École Polytechnique Montréal)

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.