On Invariance and Linear Convergence of Evolution Strategies with Augmented Lagrangian Constraint Handling

Abstract : In the context of numerical constrained optimization, we investigate stochastic algorithms, in particular evolution strategies, handling constraints via augmented Lagrangian approaches. In those approaches, the original constrained problem is turned into an unconstrained one and the function optimized is an augmented Lagrangian whose parameters are adapted during the optimization. The use of an augmented Lagrangian however breaks a central invariance property of evolution strategies, namely invariance to strictly increasing transformations of the objective function. We formalize nevertheless that an evolution strategy with augmented Lagrangian constraint handling should preserve invariance to strictly increasing affine transformations of the objective function and the scaling of the constraints—a subclass of strictly increasing transformations. We show that this invariance property is important for the linear convergence of these algorithms and show how both properties are connected.
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Pré-publication, Document de travail
2017
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Contributeur : Asma Atamna <>
Soumis le : lundi 11 décembre 2017 - 12:21:20
Dernière modification le : mardi 17 avril 2018 - 09:03:57

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  • HAL Id : hal-01660728, version 1

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Asma Atamna, Anne Auger, Nikolaus Hansen. On Invariance and Linear Convergence of Evolution Strategies with Augmented Lagrangian Constraint Handling. 2017. 〈hal-01660728〉

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