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Sufficient optimality criteria and duality for multiobjective variational control problems with $$G$$ G -type I objective and constraint functions

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  • Tadeusz Antczak

Abstract

In the paper, we introduce the concepts of $$G$$ G -type I and generalized $$G$$ G -type I functions for a new class of nonconvex multiobjective variational control problems. For such nonconvex vector optimization problems, we prove sufficient optimality conditions for weakly efficiency, efficiency and properly efficiency under assumptions that the functions constituting them are $$G$$ G -type I and/or generalized $$G$$ G -type I objective and constraint functions. Further, for the considered multiobjective variational control problem, its dual multiobjective variational control problem is given and several duality results are established under (generalized) $$G$$ G -type I objective and constraint functions. Copyright The Author(s) 2015

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  • Tadeusz Antczak, 2015. "Sufficient optimality criteria and duality for multiobjective variational control problems with $$G$$ G -type I objective and constraint functions," Journal of Global Optimization, Springer, vol. 61(4), pages 695-720, April.
    • Handle: RePEc:spr:jglopt:v:61:y:2015:i:4:p:695-720
    DOI: 10.1007/s10898-014-0203-1
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    References listed on IDEAS

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    1. K. Khazafi & N. Rueda, 2009. "Multiobjective Variational Programming under Generalized Type I Univexity," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 363-376, August.
    2. Khadija Khazafi & Norma Rueda & Per Enflo, 2010. "Sufficiency and duality for multiobjective control problems under generalized (B, ρ)-type I functions," Journal of Global Optimization, Springer, vol. 46(1), pages 111-132, January.
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    Cited by:

    1. Promila Kumar & Bharti Sharma & Jyoti Dagar, 2017. "Multi-objective semi-infinite variational problem and generalized invexity," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 580-597, September.

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