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The strict concavity is observed in Figure2.
which is unique due to the strict concavity.
Uniqueness follows from the strict concavity of g (A3).
This further reduction, is again a consequence of the strict concavity of the isoperimetric function.
which is unique due to the strict concavity of the object function.
From the strict concavity of u ˜, it follows that u ˜ ( 1 ) 1 < u ˜ η ⟺ 1 η u ˜ 1 < u ˜ η .
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Now consider the case when social welfare is the utilitarian sum of individual utilities, and all individuals have the same strictly concave utility function (strict concavity means that it displays a decreasing marginal utility).
Owing to strict concavity of the utility functions, we can conclude that the Fujigaki Sato Procedure monotonically converges to a unique stationary point and that it is stable.
Since the multi-path routing usually results in the non-strict concavity of the primal objective function, we first introduce the Proximal Optimization Algorithm to get around such difficulty.
Strict concavity or convexity means that the left side is never zero for any (tin (0,1)) unless (X=Y) and (Z=W).
By strict concavity of φ and φ (0) = 0, we obtain (7).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com