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

Author

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  • W. W. Breckner

    (Babeş-Bolyai University)

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.

Suggested Citation

  • W. W. Breckner, 1997. "Derived Sets for Weak Multiobjective Optimization Problems with State and Control Variables," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 73-102, April.
    • Handle: RePEc:spr:joptap:v:93:y:1997:i:1:d:10.1023_a:1022697700986
    DOI: 10.1023/A:1022697700986
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    Cited by:

    1. Angela Kunow & Sandy Rosche & Christiane Tammer & Christoph Weiser, 2015. "Optimal Exploitation of Nonrenewable Resources," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 928-948, December.

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