Multi objective optimization with constraints

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Manuel Oliveira
Manuel Oliveira 2017-3-15
I would like to know if anyone can help me with a multi-optimization problem using MATLAB. I have data from a spectroscopy test whose output is I [intensity] and s [the value of x-axis. I need to find a function G that satisfies the following two constraints:
where a,b and c are constants. Note: b is assumed to constant, however, it can also take the form of a polynomial of even powers e.g., a0+a1s2+a2s4+a3s6
Equation (1) is to be applied to a selected interval at the end of the data to fulfill the limit requirement.
With MATLAB I'm able to solve the integral with the function fsolve.
fun=@(x) Equation 2
[x,fval]=fsolve (Equation 2,x0)
With a ,b,and c equal to x(1),x(2),x(3) and x0 the initial guess for the parameters.
This will in fact calculate the constants a,b and c to solve the integral, however, I also need that the limit constraint be satisfied. Does any one know how I can implement this limit? I'm wondering if I can do this with this kind of expression.
q_range=q(range1:range2)
I_range=I(range1:range2)
fun=@(x)sum (Equation 1.^2)
[x2,fval]=fminsearch sum(Equation 1.^2)
Since both equations have different length does anyone know to implement both constraints using something like fgoalattain and pass as function and goal the previous expressions? Any recommendation for a different approach?
Best Regards!

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