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Anisotropic proximal gradient.

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Title: Anisotropic proximal gradient.
Authors: Laude, Emanuel1 (AUTHOR) emanuel.laude@gmail.com, Patrinos, Panagiotis1 (AUTHOR) panos.patrinos@esat.kuleuven.be
Source: Mathematical Programming. Nov2025, Vol. 214 Issue 1/2, p801-845. 45p.
Subjects: Nonconvex programming, Optimization algorithms, Numerical analysis, Mathematical programming, Logistic regression analysis
Abstract: This paper studies a novel algorithm for nonconvex composite minimization which can be interpreted in terms of dual space nonlinear preconditioning for the classical proximal gradient method. The proposed scheme can be applied to additive composite minimization problems whose smooth part exhibits an anisotropic descent inequality relative to a reference function. It is proved that the anisotropic descent property is closed under pointwise average if the Bregman distance generated by the conjugate reference function is jointly convex. More specifically, for the exponential reference function we prove its closedness under pointwise conic combinations. We analyze the method's asymptotic convergence and prove its linear convergence under an anisotropic proximal gradient dominance condition. Applications are discussed including exponentially regularized LPs and logistic regression with nonsmooth regularization. In numerical experiments we show significant improvements of the proposed method over its Euclidean counterparts. [ABSTRACT FROM AUTHOR]
Copyright of Mathematical Programming is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: This paper studies a novel algorithm for nonconvex composite minimization which can be interpreted in terms of dual space nonlinear preconditioning for the classical proximal gradient method. The proposed scheme can be applied to additive composite minimization problems whose smooth part exhibits an anisotropic descent inequality relative to a reference function. It is proved that the anisotropic descent property is closed under pointwise average if the Bregman distance generated by the conjugate reference function is jointly convex. More specifically, for the exponential reference function we prove its closedness under pointwise conic combinations. We analyze the method's asymptotic convergence and prove its linear convergence under an anisotropic proximal gradient dominance condition. Applications are discussed including exponentially regularized LPs and logistic regression with nonsmooth regularization. In numerical experiments we show significant improvements of the proposed method over its Euclidean counterparts. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Mathematical Programming is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10107-025-02204-5
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      – Code: eng
        Text: English
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        PageCount: 45
        StartPage: 801
    Subjects:
      – SubjectFull: Nonconvex programming
        Type: general
      – SubjectFull: Optimization algorithms
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Mathematical programming
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      – SubjectFull: Logistic regression analysis
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      – TitleFull: Anisotropic proximal gradient.
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              M: 11
              Text: Nov2025
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