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A Hölderian backtracking method for min-max and min-min problems

Abstract : We present a new algorithm to solve min-max or min-min problems out of the convex world. We use rigidity assumptions, ubiquitous in learning, making our method applicable to many optimization problems. Our approach takes advantage of hidden regularity properties and allows us to devise a simple algorithm of ridge type. An original feature of our method is to come with automatic step size adaptation which departs from the usual overly cautious backtracking methods. In a general framework, we provide convergence theoretical guarantees and rates. We apply our findings on simple GAN problems obtaining promising numerical results.
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Preprints, Working Papers, ...
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Contributor : Edouard Pauwels <>
Submitted on : Thursday, July 16, 2020 - 2:57:59 PM
Last modification on : Wednesday, January 20, 2021 - 3:38:26 AM
Long-term archiving on: : Monday, November 30, 2020 - 11:19:38 PM


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  • HAL Id : hal-02900875, version 1


Jérôme Bolte, Lilian Glaudin, Edouard Pauwels, Mathieu Serrurier. A Hölderian backtracking method for min-max and min-min problems. 2020. ⟨hal-02900875⟩



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