How do I optimise a nonlinear objective function which doesn't have an analytical expression

I have an objective function that for particular design variables( say s1 and s2) gives a value, but I don't exactly have any analytical expression.( It goes through a lot of nonlinear newton iteration and converges to find the a solution). How do I proceed to optimize such objective function? Its a unconstrained optimization problem. I tried using conjugate gradient, but as i don't have any analytical expression, its difficult to find alpha

Answer 1

[Sean de Wolski]

The objective function doesn't have to have an analytical expression. Write the function you wish to optimize as a function and then pass it into one of the minimizers in the Optimization Toolbox or Global Optimization Toolbox.

Optim Toolbox if your function is not discontinuous

doc fminunc

Global Optim Toolbox if the function is discontinuous:

doc patternsearch
doc ga

And in base ML:

doc fminsearch

Answer 2

[Alan Weiss]

As long as you have a program that eventually gives the value of the objective function, you can use fminsearch or (with Optimization Toolbox) fminunc to minimize the function. Just be sure to put your design variables, s1 and s2, into a vector that is usually called x.

Suppose your objective function is

 function obj = myfunction(x)
 s1 = x(1)
 s2 = x(2)
 % now do your calculations that give obj

Then to find the minimum, call

 solution = fminsearch(@myfunction,x0)

where x0 is an initial guess for the minimization. See the fminsearch function reference page or the documentation on minimizing functions of several variables.

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 3

[Ayan]

Thanks a lot!! I guess I got it