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On finding a point in the relative interior of a polyhedral set and degeneracy in geometric programming

Published online by Cambridge University Press:  17 February 2009

T. R. Jefferson  and
C. H. Scott
C. H. Scott
Affiliation:
School of Mechanical and Industrial Engineering, University of N.S.W., P.O. Box 1, Kensington, N.S.W. 2033, Australia
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Abstract

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Geometric programming is now a well-established branch of optimization theory which has its origin in the analysis of posynomial programs. Geometric programming transforms a mathematical program with nonlinear objective function and nonlinear inequality constraints into a dual problem with nonlinear objective function and linear constraints. Although the dual problem is potentially simpler to solve, there are certain computational difficulties to be overcome. The gradient of the dual objective function is not defined for components whose values are zero. Moreover, certain dual variables may be constrained to be zero (geometric programming degeneracy).

To resolve these problems, a means to find a solution in the relative interior of a set of linear equalities and inequalities is developed. It is then applied to the analysis of dual geometric programs.

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 4 , December 1978 , pp. 487 - 494
Copyright
Copyright © Australian Mathematical Society 1978

References

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