Limit subfunctions values in least square curve fitting

Hi all,

I have a function like y-theoretical=A*x+(exp(B/C)/ln(Dx)).x and y-experimental are supplied from experiment; where A=f(x,a,b,c,d); B=f(x,a,b,c,d); C=f(x,a,b,c,d); D=f(x,a,b,c,d), I have the upper and lower limits of a,b,c,d that will result to A,B,C,D and then to curve fitting of y-theoretical to y-experimental ,

my question is how to limit the values of A,B,C,D to do not be lower or exceed some specific values like 0<A<0.85; without limiting the lb or ub of a,b,c,d

Answer 1

[Matt J]

You will have to use an optimization algorithm which supports nonlinear inequality constraints, e.g., FMINCON.

Or, by analyzing f(), you must find linear or bounds constraints on a,b,c,d that imply desired bounds on A,B,C,D

[Zine]

Thanks Matt for this very interesting idea, I tried since you answered the question to understand how to use fmincon, in the help it seems exactly what I need, but the A B C D parameters are complex functions of the elementary parameters a b c d ; actually I am trying to solve a physical problem so a b c d are limited by experiment and the values resulting from the combination is also limited so any idea to set up the fmincon for this problem (I was using lsqcurvefit), thanks very much in advance

[Matt J]

your nonlcon function should look like

 function [cineq,ceq]=nonlcon(x)

      ...computations...

      upper=[A,B,C,D]-[A_ub,B_ub,C_ub,D_ub];
      lower=[A_lb,B_lb,C_lb,D_lb] -[A,B,C,D];

      ceq=[];
      cineq=[lower,upper];