Reducing Reversed Posynomial Programs

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...

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Bibliographic Details
Published inSIAM journal on applied mathematics Vol. 27; no. 4; pp. 629 - 640
Main Authors Abrams, Robert, Bunting, Marcus
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.12.1974
Subjects
Exponents
Geometric programming
Industrial engineering
Mathematical vectors
Matrices
Objective functions
Optimal solutions
Sufficient conditions
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0036-1399
1095-712X
DOI:10.1137/0127053