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A merit function approach for direct search

Gratton, Serge and Vicente, Luis A merit function approach for direct search. (2014) SIAM Journal on Optimization, 24 (4). 1980-1998. ISSN 1052-6234

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Official URL: https://doi.org/10.1137/130917661

Abstract

In this paper it is proposed to equip direct-search methods with a general procedure to minimize an objective function, possibly nonsmooth, without using derivatives and subject to constraints on the variables. One aims at considering constraints, most likely nonlinear or nonsmooth, for which the derivatives of the corresponding functions are also unavailable. The novelty of this contribution relies mostly on how relaxable constraints are handled. Such constraints, which can be relaxed during the course of the optimization, are taken care of by a merit function and, if necessary, by a restoration procedure. Constraints that are unrelaxable, when present, are treated by an extreme barrier approach. One is able to show that the resulting merit function direct-search algorithm exhibits global convergence properties for first-order stationary constraints. As in the progressive barrier method [C. Audet and J. E. Dennis Jr., SIAM J. Optim., 20 (2009), pp. 445--472], we provide a mechanism to indicate the transfer of constraints from the relaxable set to the unrelaxable one.

Item Type:Article
Additional Information:SIAM : Society for Industrial and Applied Mathematics https://epubs.siam.org/doi/abs/10.1137/130917661
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Universidade de Coimbra (PORTUGAL)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Laboratory name:
Funders:
FCT under grants PTDC/MAT/116736/2010 - FCT under grants PEst-C/MAT/UI0324/2011 - Réseau Thématique de Recherche Avancée, Fondation de Coopération Sciences et Technologies pour l’
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Deposited By: IRIT IRIT
Deposited On:10 May 2019 09:11

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