@Cryme 

g is not C^2 (already answered).

A good package that does non need C^2 and finds even global optima is DirectSearch, see
https://www.maplesoft.com/applications/view.aspx?SID=101333

@mmcdara 

Because the question was about L^* . L = A.

@tomleslie 

But solve works directly. It is evalc which does not.

You have used evalc in your previous reply, and indeed

max(evalc(s));

works there.

@tomleslie 

Of course it is a symbolic problem. Maple should try harder to identify the real numbers, and not waiting for workarounds.
Note that evalc does not always work. Try:

s:=[solve(5*(x^2-1)*(x^2-x-4)+1,explicit)];
max(s);

The integration is not complicated. u is a polynomial/r^4, so the multiple integrals can be computed symbolically.
Use rationals instead of floats.
The problem is that you have many symbolic terms so the result will be huge.

@Robert Israel 

But the best definition is of course  :-)

f := n -> (n^2+n)^2/4;

@arjangash 

Y:=numer(y)*denom(y):
CodeTools:-Usage(
SolveTools:-SemiAlgebraic([Y>0, t>0,lambda>0,c>0])
):
 memory used=484.52MiB, alloc change=113.04MiB, cpu time=4.37s, real time=4.28s, gc time=312.00ms

nops(%);
                               8

You cannot hope for nanoseconds!

@tomleslie 

It is a linear problem. simplex[maximize] finds the exact solution.

@AmusingYeti 

My remark refers to eigenvectors, not Cholesky which anyway does not apply directly to Av = aBv.

It would be interesting to see an example where eigenvalues works only after the mentioned transform.

@MDD 
{3, 4, 11}  contains the indices of the facets in the list L.

@acer 

Thanks, I forgot that simplex is still table-based, but I wonder why ":-" works in Maple 2017 and not in Maple 18 (or maybe <18 ?). I changed this in the code.

@MDD 

OK, I shall include a direct solution in your initial question https://www.mapleprimes.com/questions/223770-How-Can-Remove-The-Redundant-Inequalities

@MDD 

You may try to use the Convex package http://www-home.math.uwo.ca/~mfranz/convex/

This is just like computing m*n using the cartesian product {1,2,...,m} x {1,2,...,n}.

@carriewong