# [R] Finding solution for non-linear equations

Berend Hasselman bhh at xs4all.nl
Tue Oct 15 17:18:11 CEST 2013

```On 15-10-2013, at 15:24, Ron Michael <ron_michael70 at yahoo.com> wrote:

> Hi,
>
> I need to solve following simultaneous equations for A, B, Y1, Y2:
>
> B * Phi(Y1 - A) + (1-B) * Phi(Y1 + A) = 0.05
> B * Phi(Y2 - A) + (1-B) * Phi(Y2 + A) = 0.01
>
> Y1 <= -1.65
> Y2 >= -2.33
>
> 0 <= B <=1
>
> Phi is CDF for standard normal
>
> If there is no unique solution, then I should be able to get some feassible solution(s)
>
> Is there any way that using R I can achieve that?

You cannot solve a system of 2 equations with 4 unknowns (variables).
You can only try to find  4 values that get as close as possible (in whatever sense) to solving the system.

In other words you must define a function that returns some scalar measure of closeness to a solution.

Assuming this is homework I'll only give you a hint.

Have a look at the functions optim and constrOptim.
Both can do what you want and both are able to solve your problem.

good luck,

Berend

```