Estimating coefficients in a physical system based on observations I have a physical system which can be modelled as
$$Ax+By+C=0$$
I have thousands of measurements of $x$ and $y$ from the physical system (includes some noise).
I want to optimize for $A$, $B$, and $C$.
More Details:
$A$, $B$, and $C$ are composed of other variables which are constrained, and are the real "goal".
$$A = v_1^2 + v_1$$
$$B = v_1^2$$
$$C = v_1^2 (v_2+v_3) + v_1 v_2 + v_2 +v_3$$
$$-\pi/4 \leq v_1 \leq \pi/4$$
$$-100 \leq v_2, v_3 \leq 100$$
I would like to do this in Java (1st choice) or c++ (2nd choice).  I've found many (non)linear optimization and regression package, but the vocabulary is going over my head as to find the proper way (and therefore library+codepath) to approach solving this.

Assuming $B \neq 0$, you can rewrite this as 
$$y = A'x+C'$$
Now, you can use a least square linear regression to find the "best" value of $A'= \frac{A}{B}$ and $C'= \frac{C}{B}$
