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The ridge method for tame min-max problems

Edouard Pauwels 1
1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
IRIT - Institut de recherche en informatique de Toulouse
Abstract : We study the ridge method for min-max problems, and investigate its convergence without any convexity, differentiability or qualification assumption. The central issue is to determine whether the "parametric optimality formula" provides a conservative field, a notion of generalized derivative well suited for optimization. The answer to this question is positive in a semi-algebraic, and more generally definable, context. The proof involves a new characterization of definable conservative fields which is of independent interest. As a consequence, the ridge method applied to definable objectives is proved to have a minimizing behavior and to converge to a set of equilibria which satisfy an optimality condition. Definability is key to our proof: we show that for a more general class of nonsmooth functions, conservativity of the parametric optimality formula may fail, resulting in an absurd behavior of the ridge method.
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https://hal.archives-ouvertes.fr/hal-03186676
Contributor : Edouard Pauwels <>
Submitted on : Wednesday, March 31, 2021 - 11:43:31 AM
Last modification on : Tuesday, May 4, 2021 - 4:07:47 PM

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  • HAL Id : hal-03186676, version 1

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Edouard Pauwels. The ridge method for tame min-max problems. 2021. ⟨hal-03186676⟩

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