Efficient solution of quadratically constrained quadratic subproblems within the MADS algorithm
Nadir Amaioua (nadir.amaiouagerad.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: Cahier du Gerad, G-2016-45, 2016.
Entry Submitted: 11/17/2016
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