Lasry–Lions Envelopes and Nonconvex Optimization: A Homotopy Approach
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- Simões, Miguel
- Department of Electrical Engineering ESAT-STADIUS, KU Leuven
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- Themelis, Andreas
- 九州大学大学院システム情報科学研究院
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- Patrinos, Panagiotis
- Department of Electrical Engineering ESAT-STADIUS, KU Leuven
説明
In large-scale optimization, the presence of nonsmooth and nonconvex terms in a given problem typically makes it hard to solve. A popular approach to address nonsmooth terms in convex optimization is to approximate them with their respective Moreau envelopes. In this work, we study the use of Lasry– Lions double envelopes to approximate nonsmooth terms that are also not convex. These envelopes are an extension of the Moreau ones but exhibit an additional smoothness property that makes them amenable to fast optimization algorithms. Lasry–Lions envelopes can also be seen as an “intermediate” between a given function and its convex envelope, and we make use of this property to develop a method that builds a sequence of approximate subproblems that are easier to solve than the original problem. We discuss convergence properties of this method when used to address composite minimization problems; additionally, based on a number of experiments, we discuss settings where it may be more useful than classical alternatives in two domains: signal decoding and spectral unmixing.
収録刊行物
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- European Signal Processing Conference (EUSIPCO)
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European Signal Processing Conference (EUSIPCO) 2089-2093, 2021
Institute of Electrical and Electronics Engineers (IEEE)
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詳細情報 詳細情報について
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- CRID
- 1050861482656971136
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- ISSN
- 20761465
- 22195491
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- HANDLE
- 2324/4785493
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- 本文言語コード
- en
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- 資料種別
- conference paper
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- データソース種別
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- IRDB
