ArticleProceedings of the National Academy of Sciences of the United States of America2023
MM optimization: Proximal distance algorithms, path following, and trust regions.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.
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1 citing paper in PubMed, 6 citations in OpenAlex.
- Generalizations of the quadratic bound optimization principle.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
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3 authors at 2 institutions in 1 country.
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Abstract
We briefly review the majorization-minimization (MM) principle and elaborate on the closely related notion of proximal distance algorithms, a generic approach for solving constrained optimization problems via quadratic penalties. We illustrate how the MM and proximal distance principles apply to a variety of problems from statistics, finance, and nonlinear optimization. Drawing from our selected examples, we also sketch a few ideas pertinent to the acceleration of MM algorithms: a) structuring updates around efficient matrix decompositions, b) path following in proximal distance iteration, and c) cubic majorization and its connections to trust region methods. These ideas are put to the test on several numerical examples, but for the sake of brevity, we omit detailed comparisons to competing methods. The current article, which is a mix of review and current contributions, celebrates the MM principle as a powerful framework for designing optimization algorithms and reinterpreting existing ones.
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