ISSN:
1573-2878
Keywords:
Geometric programming
;
convex programming
;
Slater condition
;
projections
;
restrictions
;
duality
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Mathematical programming problems with unattained infima or unbounded optimal solution sets are dual to problems which lackinterior points, e.g., problems for which the Slater condition fails to hold or for which the hypothesis of Fenchel's theorem fails to hold. In such cases, it is possible to project the unbounded problem onto a subspace and to restrict the dual problem to an affine set so that the infima are not altered. After a finite sequence of such projections and restrictions, dual problems are obtained which have bounded optimal solution sets andinterior points. Although results of this kind have occasionally been used in other contexts, it is in geometric programming (both in the original psynomial form and the generalized form) where such methods appear most useful. In this paper, we present a treatment of dual projection and restriction methods developed in terms of dual generalized geometric programming problems. Analogous results are given for Fenchel and ordinary dual problems.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00933271
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