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Efficient solution of quadratically constrained quadratic subproblems within the MADS algorithm

Nadir Amaioua (nadir.amaioua***at***gerad.ca)
Charles Audet (Charles Audet gerad.ca>)
Andrew R Conn (arconn***at***us.ibm.com)
Sébastien Le Digabel (Sebastien.Le.Digabel***at***gerad.ca)

Abstract: 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 l1 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.

Keywords: Derivative-free optimization; Quadratic programming; Trust-region subproblem; Mesh Adaptive Direct Search.

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: European Journal of Operational Research, 268(1), p. 13-24, 2018.


Entry Submitted: 11/17/2016
Entry Accepted: 11/17/2016
Entry Last Modified: 02/23/2018

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