Geodesic
Bregman distance regularization for nonsmooth and nonconvex optimization
Canadian mathematical bulletin, Tome 67 (2024) no. 2, pp. 415-424

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DOI

Solving a nonsmooth and nonconvex minimization problem can be approached as finding a zero of a set-valued operator. With this perspective, we propose a novel Majorizer–Minimizer technique to find a local minimizer of a nonsmooth and nonconvex function and establish its convergence. Our approach leverages Bregman distances to generalize the classical quadratic regularization. By doing so, we generate a family of regularized problems that encompasses quadratic regularization as a special case. To further demonstrate the effectiveness of our method, we apply it on a lasso regression model, showcasing its performance.
DOI : 10.4153/S0008439523000851
Mots-clés : Bregman distance, lasso regression model, local minimizer, nonconvex optimization, nonsmooth optimization 
Mashreghi, Zeinab; Nasri, Mostafa. Bregman distance regularization for nonsmooth and nonconvex optimization. Canadian mathematical bulletin, Tome 67 (2024) no. 2, pp. 415-424. doi: 10.4153/S0008439523000851
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     author = {Mashreghi, Zeinab and Nasri, Mostafa},
     title = {Bregman distance regularization for nonsmooth and nonconvex optimization},
     journal = {Canadian mathematical bulletin},
     pages = {415--424},
     year = {2024},
     volume = {67},
     number = {2},
     doi = {10.4153/S0008439523000851},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000851/}
}
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