Dissertation/Thesis Abstract

Lagrange multipliers for set-valued functions when ordering cones have empty interior
by Tasset, Tiffany N., Ph.D., University of Colorado at Boulder, 2010, 57; 3419546
Abstract (Summary)

In set-valued optimization theory, requiring the ordering cones of the objective space and constraint space to have nonempty interiors is too restrictive for some problems. Using the quasi interior, we prove Lagrange multipliers and duality results for set-valued optimization problems when the ordering cones may have empty interiors. In the objective space, we define a new type of optimal solution for set-valued objective functions. In the constraint space, the Slater constraint is replaced by a similar constraint that uses the quasi interior. With the techniques we develop, we present new necessary and sufficient conditions for Henig efficient solutions for the optimization problem and compare them to those given in the literature. We apply our set-valued optimization theory in the setting of the optimization of functionals in vector spaces, obtaining new results and deriving theorems currently found in the literature.

Indexing (document details)
Advisor: Goodrich, Robert K.
Commitee: Corcoran, Jem N., Gustafson, Karl E., Ramsay, Arlan B., Walter, Martin E.
School: University of Colorado at Boulder
Department: Mathematics
School Location: United States -- Colorado
Source: DAI-B 71/10, Dissertation Abstracts International
Subjects: Mathematics, Theoretical Mathematics
Keywords: Cones, Duality, Henig efficient solutions, Lagrange multipliers, Quasi interior, Set-valued functions
Publication Number: 3419546
ISBN: 978-1-124-19550-6
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