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
: Thanks for any assistance you can offer.
: Dan Carlson
Try to solve the problem:
||A*x-b||**2 -> Min,
x >= c, c > 0,
where A, b, c - your known matrix and vectors.