کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
842650 908536 2010 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Duality and subdifferential for convex functions on complete CAT(0)CAT(0) metric spaces
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Duality and subdifferential for convex functions on complete CAT(0)CAT(0) metric spaces
چکیده انگلیسی

Thanks to the recent concept of quasilinearization of Berg and Nikolaev, we have introduced the notion of duality and subdifferential   on complete CAT(0)CAT(0) (Hadamard) spaces. For a Hadamard space XX, its dual is a metric space X∗X∗ which strictly separates non-empty, disjoint, convex closed subsets of XX, provided that one of them is compact. If f:X→(−∞,+∞]f:X→(−∞,+∞] is a proper, lower semicontinuous, convex function, then the subdifferential ∂f:X⇉X∗∂f:X⇉X∗ is defined as a multivalued monotone operator such that, for any y∈Xy∈X there exists some x∈Xx∈X with xy⃗∈∂f(x). When XX is a Hilbert space, it is a classical fact that R(I+∂f)=XR(I+∂f)=X. Using a Fenchel   conjugacy-like concept, we show that the approximate subdifferential ∂ϵf(x)∂ϵf(x) is non-empty, for any ϵ>0ϵ>0 and any xx in efficient domain of ff. Our results generalize duality and subdifferential of convex functions in Hilbert spaces.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 73, Issue 10, 15 November 2010, Pages 3450–3455
نویسندگان
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