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The Proximal Subgradient and Constancy
Published online by Cambridge University Press: 20 November 2018
Abstract
If f is a lower semicontinuous function mapping a connected open subset of ℝn to (—∞, ∞], and if the proximal subgradient of f reduces to zero wherever it exists, then f is constant.
Résumé
Soit f une fonction semicontinue inférieurement de U à (—∞, ∞], où U est un ensemble ouvert et connexe de ℝn. Si tout sousgradient proximal de f est nul, alors f est constante.
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- Research Article
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- Copyright © Canadian Mathematical Society 1993
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