system of linear equations but with condtions that all variables should be > 0

I have the following system of linear equations

x - 2y - 3z = 5

-5x + y - 4z = 20

-3x -4y + z = 49

I want to solve for x,y, and z but want those to be greater than 0.

Adding conditions for x>=0, y>=0, and z>=0.

It's shown here only as a sample of 3 equations, but I have to deal with 184 equations and 184 variables which need to be greater or equal to 0.

Thanks, Julio Fernandez

[Walter Roberson]

Will you always have N linear equations in N unknowns? And the rank() will be N? If so, then if the straightforward use of the mldivide ('\') operator does not give you non-negative solutions then the equations are not solvable under the additional conditions.

[Azzi Abdelmalek]

That's why I've suggested A\b. Maybe he wants to take the solution, only when his conditions are true.

Answer 1

[Shashank Prasanna]

If you'd like to add positive constraints then you can use a solver in the Optimization Toolbox called LSQNONNEG. If you'd like to add more generic constraints you can use LSQLIN

http://www.mathworks.com/help/optim/ug/lsqnonneg.html

http://www.mathworks.com/help/optim/ug/lsqlin.html

There isn't a way to do this from base MATLAB, unless you code it yourself.

Answer 2

[Azzi Abdelmalek]

For a system A*x=b the solution is

x=A\b