Derived Sets for Weak Multiobjective Optimization Problems with State and Control Variables

W. W. Breckner
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W. W. Breckner: Babeş-Bolyai University

Journal of Optimization Theory and Applications, 1997, vol. 93, issue 1, No 5, 73-102

Abstract: Abstract The concept of a K-gradient, introduced in Ref. 1 in order to generalize the concept of a derived convex cone defined by Hestenes, is extended to weak multiobjective optimization problems including not only a state variable, but also a control variable. The new concept is employed to state multiplier rules for the local solutions of such dynamic multiobjective optimization problems. An application of these multiplier rules to the local solutions of an abstract multiobjective optimal control problem yields general necessary optimality conditions that can be used to derive concrete maximum principles for multiobjective optimal control problems, e.g., problems described by integral equations with additional functional constraints.

Keywords: Multiobjective optimization; multiobjective optimal control; necessary optimality conditions (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022697700986

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