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On efficiency and mixed duality for a new class of nonconvex multiobjective variational control problems

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  • Tadeusz Antczak

Abstract

In this paper, we extend the notions of $$(\Phi ,\rho )$$ ( Φ , ρ ) -invexity and generalized $$(\Phi ,\rho )$$ ( Φ , ρ ) -invexity to the continuous case and we use these concepts to establish sufficient optimality conditions for the considered class of nonconvex multiobjective variational control problems. Further, multiobjective variational control mixed dual problem is given for the considered multiobjective variational control problem and several mixed duality results are established under $$(\Phi ,\rho )$$ ( Φ , ρ ) -invexity. Copyright The Author(s) 2014

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  • Tadeusz Antczak, 2014. "On efficiency and mixed duality for a new class of nonconvex multiobjective variational control problems," Journal of Global Optimization, Springer, vol. 59(4), pages 757-785, August.
    • Handle: RePEc:spr:jglopt:v:59:y:2014:i:4:p:757-785
    DOI: 10.1007/s10898-013-0092-8
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    References listed on IDEAS

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    1. Igor V. Konnov & Dinh The Luc & Alexander M. Rubinov, 2006. "Generalized Convexity and Related Topics," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-37007-9, October.
    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. Savin Treanţă, 2021. "Duality Theorems for ( ρ , ψ , d )-Quasiinvex Multiobjective Optimization Problems with Interval-Valued Components," Mathematics, MDPI, vol. 9(8), pages 1-12, April.
    2. Jayswal, Anurag & Singh, Shipra & Kurdi, Alia, 2016. "Multitime multiobjective variational problems and vector variational-like inequalities," European Journal of Operational Research, Elsevier, vol. 254(3), pages 739-745.
    3. Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2015. "Some quantum integral inequalities via preinvex functions," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 242-251.
    4. Cristescu, Gabriela & Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2016. "Some inequalities for functions having Orlicz-convexity," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 226-236.
    5. 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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