MATLAB: Solving overdeterminated linear equation system with specified conditions

boundary conditionoverdeterminated systemsolve

Dear fellows! I´m new in the world of matlab and i´d like to solve the following overdeterminated system of linear equations with lsqr-method.

A*p=b

where A is a (5×3) matrix, p=[p1;p2;p3] and b is vector with 5 given vector elements.

without any conditions i could solve the system with p=A\b or p=lsqr(A,b).

BUT following conditions have to be achivied for solving the problem

1. p1;p2;p3 are always >=0

2. p1+p2+p3=sum(p)=1

Does sombody can help me to set the conditions for the solving process?

best regards Thomas

Hi Thomas, If you have the Optimization Toolbox, LSQLIN can solve constrained least-squares problems: http://www.mathworks.com/help/toolbox/optim/ug/lsqlin.html

You can use the A and b arguments to enforce that p1; p2; p3 >= 0 and the Aeq and beq arguments to enforce that p1+p2+p3 = 1.

Your objective function will be passed a single variable which is a vector of values. It will not be passed two scalars.

function f = objfun(x)
x1 = x(1); x2 = x(2);
a1=1;
a2=5;
a3=-4;
b1=1;
b2=2;
f=a1*(x1-b1)*(x1-b1)+a2*(x2-b2)*(x2-b2)+a3*x1*x2;
end

 Aeq=zeros(size(x));
 Aeq(1:7)=1;
 beq=0;