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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 $b \geq 0$

$2 - 3m -c \geq 0$

$2 - 3m -c \leq b(\sqrt(1+m^2))$

$4 yi - 7m xi*m -c \geq 0$ for all i

$4 yi - 7m xi*m -c \leq b(\sqrt(1+m^2))$ 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.

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# linear objective function, non-linear constraints involving square-root of variables

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 $b \geq 0$

$2 - 3m -c \geq 0$

$2 - 3m -c \leq b(\sqrt(1+m^2))$

$4 - 7m -c \geq 0$

$4 - 7m -c \leq b(\sqrt(1+m^2))$

....