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On duality for convex minimization with nested maxima

Published online by Cambridge University Press:  17 February 2009

C. H. Scott ,
T. R. Jefferson  and
E. Sirri
C. H. Scott
Affiliation:
Graduate School of Management, University of California, Irvine, California 92715, U.S.A.
T. R. Jefferson
Affiliation:
Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, U.S.A.
E. Sirri
Affiliation:
Graduate School of Management, University of California, Irvine, California 92715, U.S.A.
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Abstract

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In this paper, we consider convex programs with linear constraints where the objective function involves nested maxima of linear functions as well as a convex function. A dual program is constructed which has interpretational significance and may be easier to solve than the primal formulation. A numerical example is given to illustrate the method.

Type
Research Article
Information
The ANZIAM Journal , Volume 26 , Issue 4 , April 1985 , pp. 517 - 522
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Fenchel, W., Convex cones, sets and functions (Princeton University, 1953).Google Scholar
[2]Murtagh, B. A. and Saunders, M. A., “Large scale linearly constrained optimization”, Math. Programming 14 (1978), 44–72.Google Scholar
[3]Peterson, E. L., “Geometric programming”, SIAM Rev. 18 (1976), 1–52.Google Scholar
[4]Rockafellar, R. T., Convex analysis (Princeton University, 1970).Google Scholar