MATLAB: Which function should i use in Optimization toolbox

optimization

i have a function let say f= 2*x1*x2 + x1^2 – x1 – 2*x2 + …

(note that the function can not be displayed by matlab because it is the result of inverse matrix, and it is very, very long)

i want to optimize f so it tends to zero (minimize) lower bound for either x1 and x2 is 0.1*x upper bound for either x1 and x2 is 10*x

there is optimization toolbox installed, but i am not sure which function should i use.

Best regards, Dahnial

fmincon

This kind of system can be programmed by introducing up to 4 new integer variables, with the logical conditions

x1 == x6 * x4
x1 == x7 * x5
x2 == x8 * x4
x2 == x9 * x5

You would then follow that by reducing the original equations, replacing each x1 by x6 * x4 and each x2 by x8 * x4 everywhere the equations,

Then you would add the nonlinear equality constraints

x6 * x4 - x7 * x5
x8 * x4 - x9 * x5

The list of variables would be x3, x4, x5, x6, x7, x8, x9 with x4 through x9 all integer variables (so x3 is the only non-integer variable.)

I know your original list did not require x5 to be integer, but your integer constraints on the other variables require that x5 be integer, I figure.