The ridge method for tame min-max problems - Intelligence Artificielle Access content directly
Preprints, Working Papers, ... Year : 2022

The ridge method for tame min-max problems


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.
Fichier principal
Vignette du fichier
partialMinimization.pdf (459.12 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03186676 , version 1 (31-03-2021)
hal-03186676 , version 2 (04-02-2022)
hal-03186676 , version 3 (26-12-2022)
hal-03186676 , version 4 (23-06-2023)



Edouard Pauwels. The ridge method for tame min-max problems. 2022. ⟨hal-03186676v2⟩
240 View
176 Download



Gmail Facebook X LinkedIn More