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Journal Articles Theoretical Computer Science Year : 2020

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

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Asma Atamna
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  • PersonId : 736387
  • IdHAL : asma-atamna
Anne Auger
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  • PersonId : 751513
  • IdHAL : anne-auger
Nikolaus Hansen

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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Dates and versions

hal-01660728 , version 1 (11-12-2017)
hal-01660728 , version 2 (26-09-2018)
hal-01660728 , version 3 (26-02-2020)

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Asma Atamna, Anne Auger, Nikolaus Hansen. On Invariance and Linear Convergence of Evolution Strategies with Augmented Lagrangian Constraint Handling. Theoretical Computer Science, 2020, 832, pp.68-97. ⟨10.1016/j.tcs.2018.10.006⟩. ⟨hal-01660728v3⟩
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