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Subdifferential test for optimality

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Abstract

We provide a first-order necessary and sufficient condition for optimality of lower semicontinuous functions on Banach spaces using the concept of subdifferential. From the sufficient condition we derive that any subdifferential operator is monotone absorbing, hence maximal monotone when the function is convex.

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Authors and Affiliations

  1. Université des Antilles et de la Guyane, 97159, Pointe à Pitre, France

    Florence Jules & Marc Lassonde

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  1. Florence Jules
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  2. Marc Lassonde
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Correspondence to Marc Lassonde.

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Jules, F., Lassonde, M. Subdifferential test for optimality. J Glob Optim 59, 101–106 (2014). https://doi.org/10.1007/s10898-013-0078-6

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  • DOI: https://doi.org/10.1007/s10898-013-0078-6

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