i am trying to solve a general linear objective function with non-linear constraints. Can someone help me solve this. Here is an example of one problem i am trying to solve,

minimize $b$

subject to $b \geq 0$

$yi - xi*m -c \geq 0$ for all i

$yi - xi*m -c \leq b(\sqrt(1+m^2))$ for all i

(xi,yi) = (1,2), (3,5), (9,7), (6,8), (7,6.5), (3,5.8), (10,19), (4,6)

The above problem is an example of what I am trying to solve. The number of (xi,yi) values is in the range of thousands for the real problem.