Consider the following optimization problem with $A > 0$, $B > 0$, $b_i \geq 0$ and each $f_i(x_i)$ being convex functions. Is there any good algorithm for solving this problem?
$\min_{x,y} \sum_i f_i(x_i)y_i$
s.t.
$\sum_i x_i \leq A$,
$\sum_i b_iy_i \leq B$,
$x_i \geq 0$,
$0 \leq y_i \leq 1$.