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.
|Advisor:||Goodrich, Robert K.|
|Commitee:||Corcoran, Jem N., Gustafson, Karl E., Ramsay, Arlan B., Walter, Martin E.|
|School:||University of Colorado at Boulder|
|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|
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