Re: A not so easy problem about concavity

Dear All,

Let X in or equal to R^n be a nonempty, convex and compact set, and
consider the function f: X x X --> R defined by

f(u,v) := ((a*b)/2)*|v|^2 - (a/2)*|u|^2 - (1/2)*|v-g(u)|^2,

where g:X --> X is twice continuously differentiable, b is a parameter
in the interval (0,1), a is a positive parameter, and |.| denotes the
Euclidean norm.

My question is: is it possible to find values for the parameters a and
b such that f is strictly concave on u and v?

Thanks in advance,

Paul

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