Group for Research in Decision Analysis

# Efficient solution of quadratically constrained quadratic subproblems within a direct-search algorithm

## Nadir Amaioua, Charles Audet, Andrew R. Conn, and Sébastien Le Digabel

The Mesh Adaptive Direct Search algorithm (MADS) is an iterative method for constrained blackbox optimization problems. One of the optional MADS features is a versatile search step in which quadratic models are built leading to a series of quadratically constrained quadratic subproblems. This work explores different algorithms that exploit the structure of the quadratic models: the first one applies an $$l_1$$ exact penalty function, the second uses an augmented Lagrangian and the third one combines the former two, resulting in a new algorithm. These methods are implemented within the NOMAD software package and their impact are assessed through computational experiments on 65 analytical test problems and 4 simulation-based engineering applications.

, 17 pages

This cahier was revised in November 2016