A Chain Rule for Essentially Smooth Lipschitz Functions
نویسندگان
چکیده
منابع مشابه
Essentially Smooth Lipschitz Functions
In this paper we address some of the most fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on separable Banach spaces. For example, we examine the relationship between integrability, D-representability, and strict differentiability. In addition to this, we show that on any separable Banach space there is a significant family of locally Lipsc...
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In this paper we address some of the most fundamental questions regarding the diierentiability structure of locally Lipschitz functions deened on Banach spaces. For example, we examine the relationship between inte-grability, D-representability and strict diierentiability. In addition to this, we show that on a large class of Banach spaces there is a signiicant family of locally Lipschitz funct...
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Motivated by an attempt to find a general chain rule formula for differentiating the composition f ◦ g of Lipschitz functions f and g that would be as close as possible to the standard formula (f ◦ g)′(x) = f ′(g(x)) ◦ g′(x), we show that this formula holds without any artificial assumptions provided derivatives are replaced by complete derivative assignments. The idea behind these assignments ...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 1998
ISSN: 1052-6234,1095-7189
DOI: 10.1137/s1052623496297838