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I want to minimize and objective function $\hat{B_i}$ $i\in l$, which can be computed by a matlab code (assume $\operatorname{findB}(a, b, c)$ returns $B$. I have the following optimization problem:

$$\begin{array}{rl} \min & \sum\limits_{i\in l} \hat{B_i}(a_i,b_i, c_i) \\ \text{s.t.} & \sum\limits_{i\in l} a_i \leq A \\ & \sum\limits_{i\in l} b_i \leq B \\ & \sum\limits_{i\in l} c_i = C \\ & a_i,b_i \in\mathbb Z^+, c_i\ge0 \qquad \forall i\in l \\ \end{array}$$

How can I solve this in Matlab or in another platform? Note that I do not have a close form expression for $B$. For a sample calculations, I can assume $A = 20, B=25, C=30$

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