Reducing Reversed Posynomial Programs

Abstract

In this paper we study degeneracy in reversed posynomial programming. The word “degeneracy” was used in the original development of geometric (prototype posynomial) programming to describe a program in which a term will approach zero in an optimal sequence. A generalization of the original meaning to include reversed constraints is given. Corresponding to each degenerate reversed program, a unique reduced form is determined from the matrix of exponents by dropping specified terms and constraints. It is shown that, subject to a constraint qualification, the reduced and original programs have equal infima. A condition for boundedness of maximization problems subject to prototype constraints is given. Also, sufficient conditions are presented which guarantee that an optimal solution will be achieved and will occur at a point at which all variables are strictly positive.