The continous Legendre transform, its inverse transform, and applications
نویسندگان
چکیده
منابع مشابه
The Legendre transform
f((1− t)x1 + tx2) ≤ (1− t)f(x1) + tf(x2), x1, x2 ∈ C, 0 ≤ t ≤ 1, then f : X → R is convex. Proof. Let (x1, α1), (x2, α2) ∈ epi f and 0 ≤ t ≤ 1. The fact that the pairs (xi, αi) belong to epi f means in particular that f(xi) < ∞, and hence that xi ∈ C, as otherwise we would have f(xi) =∞. But (1− t)(x1, α1) + t(x2, α2) = ((1− t)x1 + tx2, (1− t)α1 + tα2), and, as x1, x2 ∈ C, f((1− t)x1 + tx2) ≤ (...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1980
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s016117128000004x