A CONVEX APPROXIMANT METHOD FOR NON-CONVEX EXTENSIONS OF GEOMETRIC PROGRAMMING
Management sciences research rept.
CARNEGIE INST OF TECH PITTSBURGH PA GRADUATE SCHOOL OF INDUSTRIAL ADMINISTRATION
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Many important problems of engineering and management are of a form which could be represented as geometric programs except that the functional to be minimized as well as the constraints are not confined to posynomials in that some of the coefficients are negative. This paper supplies a way for dealing with such negative terms by a constraint adjunction procedure which yields an associated approximating problem involving only polynomials which can, in turn, be transformed into a convex programming problem that has only one local global optimum. The latter, which is called a convex approximant, has an associated dual. Recourse to the related duality theory then supplies guidance for improving the approximation along lines that are indicated in the paper.
- Administration and Management
- Operations Research