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Let (X= [ {a,b} ]), (alpha=1), (m=1 ) and f, g be two concave functions for all (x in X).
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Since secrecy capacity is the difference of two concave functions, it is a non-convex optimization in general.
The measure distortions are two increasing concave/convex functions of the positive half line that are bounded below/above by the identity.
Let (f(x)) and (g(x)) be any two smooth concave functions on the interval I and (h(x)) be a non-negative weight function satisfying (2.1).
Let, be nonnegative concave functions on.
Given x t, we generate the next iterate x t +1 with the following update In our case, our log likelihood is concave differentiable, and there are three convex continuous functions: g1, g2 and g3, corresponding to each regularization term.
where both u and g are increasing, concave functions.
Let ψ ̃ be a concave function on [0, 1].
As the resource allocation is designed on the basis of convex optimization, the service quality has to be concave function which has zero or negative second derivation.
There are two factors explaining the concave curves.
Therefore, the utilities are concave functions on electricity prices.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com