MATLAB: How to solve a system of equations with a constraint

constraintfsolvelsqnonlinsystem equations

Hello, I'm new to MATLAB and I'm looking for a way to solve the system below:

w=lambda^(-1)*covmat^(-1)*(meanbl-(vec1'*covmat^(-1)*vec1)^(-1)*(vec1'*covmat^(-1)*meanbl-lambda)*vec1)

H=w'*meanbl+phi*sqrt(w'*covmat*w)

Where I want to find w (n-element vector) and phi (scalar). The constraint is that all the elements of w and also phi have to be positive. lambda and H are scalars, covmat is a nxn matrix, and meanbl and vec1 are n-element vectors.

I'm aware that fsolve does not allow for constraints, but I'm not being able to use lsqnonlin.

Thank you very much.

Best Answer

Instead of w and phi, use w.^2 and phi^2 in your system.

This ensures that the unknowns are nonnegative.

Best wishes

Torsten.

Related Solutions

MATLAB: How to use lsqnonlin together with MultiStart

First you need to figure out bounds on all the parameters w and lambda. In general, it is not enough to say that lb = zeros(n+1,1), you also need an upper bound vector.

Once you have that, you can set up your problem for MultiStart easily. You just need to put your problem into a problem structure using the createOptimProblem function:

 problem = createOptimProblem('lsqnonlin','x0',x0,'lb',lb,'ub',ub,'objective',@sub);
 ms = MultiStart;
 [x,fval,eflag,output,manymins] = run(ms,problem,50);

Alan Weiss

MATLAB mathematical toolbox documentation

MATLAB: How to implement a nonlinear constraint

    for i=1:T-M    
    objective = @(w) -(zbarA3(:,i)'*w - rf)/(sqrt(w'*covmatA3{1,i}*w));
    w0 = Wi_AQ2;
    Aeq = ones(1,n);
    beq = 1;
    W_Q3(:,i) = fmincon(objective,w0,[],[],Aeq,beq,[],[], @(w) nonling(w,w0) );
    end 
    function [c,ceq]=nonling(w,w0)
      c= .005^2-norm(w - w0)^2 ;
      ceq=[];
    end

Best Answer

Related Solutions

MATLAB: How to use lsqnonlin together with MultiStart

MATLAB: How to implement a nonlinear constraint

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