Abstract convex optimal antiderivatives
نویسندگان
چکیده
منابع مشابه
How to compute antiderivatives
The roots of this problem go back to the beginnings of calculus and it is even sometimes called “Newton’s problem”. Historically, it has played a major role in the development of the theory of the integral. For example, it was Lebesgue’s primary motivation behind his theory of measure and integration. Indeed, the Lebesgue integral solves the primitive problem for the important special case when...
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Since we have the same product rule, quotient rule, sum rule, chain rule etc. available to us for differentiating complex functions, we already know many antiderivatives. For example, by differentiating f (z) = z one obtains f ′(z) = nzn−1, and from this one sees that the antiderivative of z is 1 n+1 z – except for the very important case where n = −1. Of course that special case is very import...
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fi = inf( p(x) : g(x) E 4, x E R 1, P) where S is an arbitrary convex cone in a finite dimensional space, R is a convex set, and p and g are respectively convex and S-convex (on a), were given in [lo]. These characterizations hold without any constraint qualification. They use the “minimal cone” .S’ of (P) and the cone of directions of constancy D;(S’). In the faithfully convex case these cones...
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ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2012
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2012.01.004