Solving overdeterminated linear equation system with specified conditions

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 (5x3) 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

Answer 1

[Seth DeLand]

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.

[Thomas]

Thank you for your answer.

Did i define the constraints correct for following settings?

(C(5x3)matrix, d(5x1)vector) and C*x=d)

where

lb=zeros(3,1); %x1,x2,x3>=0

Aeq=ones(1,3);beq=1; %x1+x2+x3=1

[x,resnorm,residual,exitflag,output]=lsqlin(C,d,[],[],Aeq,beq,lb);

best regards

Thomas