On solving optimization problems with proportion-constraints

The purpose of this paper is to establish sufficient conditions for the existence of solutions to mathematical programs where the variables of the solution satisfy given proportions. These conditions rely on convergence properties of powers of nonnegative matrices when these powers form a bounded sequence. We assume that if an arbitrary vectorx is premultiplied by elements of this sequence, the limit of the sequence (which might be a Cesaro (C, 1) limit) gives an improvement of the objective.This research was supported by NSF Grants ENG 76-15599 and ENG76-12266 and ONR Contract N00014-75-C-0493.