Constrained minimization problem : fmincon function

Hi all,

I want to find a solution to this equation with adding some assumptions:

       MATA * Xsol = MATd 

 where MATA is 1400x12 matrix , MATd is a vector with size 1400 
 and Xsol =(Xsol(1),Xsol(2),Xsol(3),Xsol(4),Xsol(5),Xsol(6),Xsol(7),Xsol(8),Xsol(9),Xsol(10),Xsol(11),Xsol(12))

I resolved this equation with pinv:

Xsol = pinv(MATAA)*MATd;

But I need some assumptions to add them to my solution. Which are :

    dot([ Xsol(1) Xsol(4) Xsol(7)],[ Xsol(2) Xsol(5) Xsol(8)]) =0 ;

    dot([ Xsol(1) Xsol(4) Xsol(7)],[ Xsol(3) Xsol(6) Xsol(9)]) =0 ;

    dot([ Xsol(3) Xsol(6) Xsol(9)],[ Xsol(2) Xsol(5) Xsol(8)]) =0 ;

So I will use now the fmincon function to solve the constrained minimization problem. First step I get the starting guess with :

 Xsol0 = pinv(MATAA)*MATd;
options = optimoptions(@fmincon,'Algorithm','sqp','MaxFunEvals', 3000 );
[Xsol,fval] =  fmincon(@objfun,Xsol0,[],[],[],[],[],[],@confun,options);

I define confun.m for the nonlinear constraints.

 function [c,ceq] = confun(Xsol)
c=[];
ceq(1)=dot([ Xsol(1) Xsol(4) Xsol(7)],[ Xsol(2) Xsol(5) Xsol(8)]) ;
ceq(2)=dot([ Xsol(1) Xsol(4) Xsol(7)],[ Xsol(3) Xsol(6) Xsol(9)]) ;
ceq(3)=dot([ Xsol(3) Xsol(6) Xsol(9)],[ Xsol(2) Xsol(5) Xsol(8)]);
 end

But How can I define my objective function ?? to obtain Xsol with the assumptions ?

     function f = objfun(Xsol)
    ????
    ?????
    end

Any help please?

Answer 1

[Matt J]

Why not a least squares objective as I suggested to you in your previous post on the subject

    function fval=objfun(Xsol)

      fval=norm( MATA * Xsol - MATd ).^2

   end

In the original version of your problem, you are calculating a least squares solution, so why not use a least squares objective function here as well?