Posted by N. Khokhlov on December 10, 1997 at 10:58:32:

In Reply to: Constrained linear system problem posted by Dan Carlson on December 03, 1997 at 18:45:57:

: I have an overdetermined linear system I need to solve that

: has a physical constraint imposed upon its solution. All of

: the elements of the solution vector must be greater than zero.

: Being a real-world problem, there is noise in the data that

: cannot be eliminated. The simple approaches I have tried

: for solving the linear system always result in at least a few

: negative solution vector elements. The residual error is

: sufficiently small, but the solutions are still unacceptable

: because they violate the physical constraint.

: Is this problem best handled as a linear system problem, or

: as a linear programming problem? If it is best handled as a

: linear system problem, then what is the best method of

: solution?

: Thanks for any assistance you can offer.

: Dan Carlson

: dcarlson@stb.com

Try to solve the problem:

||A*x-b||**2 -> Min,

x >= c, c > 0,

where A, b, c - your known matrix and vectors.