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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Symmetrized separable convex programming


Author: L. McLinden
Journal: Trans. Amer. Math. Soc. 247 (1979), 1-44
MSC: Primary 90C25
DOI: https://doi.org/10.1090/S0002-9947-1979-0517685-5
MathSciNet review: 517685
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Abstract: The duality model for convex programming studied recently by E. L. Peterson is analyzed from the viewpoint of perturbational duality theory. Relationships with the traditional Lagrangian model for ordinary programming are explored in detail, with particular emphasis placed on the respective dual problems, Kuhn-Tucker vectors, and extremality conditions. The case of homogeneous constraints is discussed by way of illustration. The Slater existence criterion for optimal Lagrange multipliers in ordinary programming is sharpened for the case in which some of the functions are polyhedral. The analysis generally covers nonclosed functions on general spaces and includes refinements to exploit polyhedrality in the finite-dimensional case. Underlying the whole development are basic technical facts which are developed concerning the Fenchel conjugate and preconjugate of the indicator function of an epigraph set.


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DOI: https://doi.org/10.1090/S0002-9947-1979-0517685-5
Keywords: Nonlinear programming, Lagrangian duality, nonclosed functions, general spaces, projected model
Article copyright: © Copyright 1979 American Mathematical Society