Are all elements of a always >= 0? I will assume so.

I’m not sure this is exactly what you want, but presuming I understand your notation,I think you want something like

variables x(n) y(x) z(n)
for i = 1:n
{y(i), beta*x(i), z(i)} == exponential{1}
end
% Now replace y(i)*exp(beta*x(i)/y(i)) by z(i)
% and form the constraint
a'*(z - x) - c <= 0 % fix this up if it's not quite right

I’ll let you figure out whether there is a short cut such as {y, beta*x, z} == exponential(n}
instead of the for loop.

Edit: Note I just corrected a typo:{ rather than ( in what should be exponential{1}

Assumption is a \geq 0. The notation \odot means componentwise multiplication and \oslash means componentwise division, which I think you might have understood correctly