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Communication Dans Un Congrès Année : 2019

How to globally solve non-convex optimization problems involving an approximate ℓ 0 penalization

Résumé

For dealing with sparse models, a large number of continuous approximations of the 0 penalization have been proposed. However, the most accurate ones lead to non-convex optimization problems. In this paper, by observing that many such approximations are piecewise rational functions, we show that the original optimization problem can be recast as a multivariate polynomial problem. The latter is then globally solved by using recent optimization methods which consist of building a hierarchy of convex problems. Finally, experimental results illustrate that our method always provides a global optimum of the initial problem for standard 0 approximations. This is in contrast with existing local algorithms whose results depend on the initialization.
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Dates et versions

hal-02196878 , version 1 (29-07-2019)

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Arthur Marmin, Marc Castella, Jean-Christophe Pesquet. How to globally solve non-convex optimization problems involving an approximate ℓ 0 penalization. ICASSP 2019 : IEEE International Conference on Acoustics, Speech and Signal Processing, May 2019, Brighton, United Kingdom. pp.5601-5605, ⟨10.1109/ICASSP.2019.8683692⟩. ⟨hal-02196878⟩
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