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Duality theorems for a new class of multitime multiobjective variational problems

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  • Ariana Pitea
  • Mihai Postolache

Abstract

In this work, we consider a new class of multitime multiobjective variational problems of minimizing a vector of functionals of curvilinear integral type. Based on the normal efficiency conditions for multitime multiobjective variational problems, we study duals of Mond-Weir type, generalized Mond-Weir-Zalmai type and under some assumptions of (ρ, b)-quasiinvexity, duality theorems are stated. We give weak duality theorems, proving that the value of the objective function of the primal cannot exceed the value of the dual. Moreover, we study the connection between values of the objective functions of the primal and dual programs, in direct and converse duality theorems. While the results in §1 and §2 are introductory in nature, to the best of our knowledge, the results in §3 are new and they have not been reported in literature. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Ariana Pitea & Mihai Postolache, 2012. "Duality theorems for a new class of multitime multiobjective variational problems," Journal of Global Optimization, Springer, vol. 54(1), pages 47-58, September.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:1:p:47-58
    DOI: 10.1007/s10898-011-9740-z
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    References listed on IDEAS

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    1. T. Antczak, 2005. "Modified Ratio Objective Approach in Mathematical Programming," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 23-40, July.
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    Cited by:

    1. 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.
    2. Tiziana Ciano & Massimiliano Ferrara & Ştefan Mititelu & Bruno Antonio Pansera, 2020. "Efficiency for Vector Variational Quotient Problems with Curvilinear Integrals on Riemannian Manifolds via Geodesic Quasiinvexity," Mathematics, MDPI, vol. 8(7), pages 1-15, June.
    3. Muhammad Aslam Noor & Khalida Inayat Noor & Saima Rashid, 2018. "Some New Classes of Preinvex Functions and Inequalities," Mathematics, MDPI, vol. 7(1), pages 1-16, December.
    4. 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.
    5. 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.
    6. Ramu Dubey & Lakshmi Narayan Mishra & Luis Manuel Sánchez Ruiz & Deepak Umrao Sarwe, 2020. "Nondifferentiable Multiobjective Programming Problem under Strongly K - G f -Pseudoinvexity Assumptions," Mathematics, MDPI, vol. 8(5), pages 1-11, May.

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