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Characterizations of optimality for continuous convex mathematical programs. Part I. Linear constraints

Published online by Cambridge University Press:  17 February 2009

T. R. Jefferson
Affiliation:
School of Mechanical and Industrial Engineering, University of N.S.W., Kensington, N.S.W. 2033
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Abstract

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Recently we have developed a completely symmetric duality theory for mathematical programming problems involving convex functionals. Here we set our theory within the framework of a Lagrangian formalism which is significantly different to the conventional Lagrangian. This allows various new characterizations of optimality.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Rockafellar, R. T., “Integrals which are convex functionals”, Pacific J. Math. 24 (1968), 525539.CrossRefGoogle Scholar
[2]Rockafellar, R. T., “Convex integral functionals and duality”, in Contributions to nonlinear functional analysis (New York: Academic Press, 1971), pp. 215236.CrossRefGoogle Scholar
[3]Rockafellar, R. T., “Conjugate duality and optimization”, SIAM Regional Conference Series in Applied Mathematics, 16 (1974).Google Scholar
[4]Scott, C. H. and Jefferson, T. R., “A generalization of geometric programming with an application to information theory”, Information Sciences 12 (1977), 263269.CrossRefGoogle Scholar
[5]Scott, C. H. and Jefferson, T. R., “Duality in infinite-dimensional mathematical programming: Convex integral functionals”, J. Math. Anal. Appl. 61 (1977), 251261.CrossRefGoogle Scholar
[6]Scott, C. H. and Jefferson, T. R., “Characterizations of optimality for continuous convex mathematical programs. Part 2. Nonlinear constraints” (in preparation).Google Scholar