The Application of Generalized Geometric Programming (Conjugate Duality) to the Analysis and Solution of Convex Programs.
Final technical rept. 16 Jul 83-15 Jul 85,
PITTSBURGH UNIV PA DEPT OF INDUSTRIAL ENGINEERING
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The research in this grant involves the application of generalized geometric programming conjugate duality to a variety of problems. The duality theory constructs a dual program which can provide insight into the problem and assist in solution. Composite geometric programming was developed as an important new class of mathematical programming was developed as an important new class of mathematical programs. Applications studied included machining economics, resource allocation, assignment, nonlinear multicommodity network flow problems, mineral processing, statistical analysis of ordinal categorical data, and estimation. Geometric programming was extended from functions of posynomial form to functions which include exponential, logarithmic and other factors by the development of composite geometric programming. This class retains the power of geometric programming while addressing new problems. Certain machining economics problems and chemical equilibrium problems fall into this new class of mathematical programs. Research on the machining economics problem resulted in the problem being reduced from a nonlinear program to a one-dimensional search. In addition, duality theory provided easy parametric analysis.
- Statistics and Probability