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First and Second Order Optimality Conditions Using Approximations for Nonsmooth Vector Optimization in Banach Spaces

Author

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  • P. Q. Khanh

    (International University of Hochiminh City)

  • N. D. Tuan

    (University of Natural Sciences of Hochiminh City)

Abstract

We use the first and second order approximations of mappings to establish both necessary and sufficient optimality conditions for unconstrained and constrained nonsmooth vector optimization problems. Ideal solutions, efficient solutions, and weakly efficient solutions are considered. The data of the problems need not even be continuous. Some often imposed compactness assumptions are also relaxed. Examples are provided to compare our results and some known recent results.

Suggested Citation

  • P. Q. Khanh & N. D. Tuan, 2006. "First and Second Order Optimality Conditions Using Approximations for Nonsmooth Vector Optimization in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 289-308, August.
    • Handle: RePEc:spr:joptap:v:130:y:2006:i:2:d:10.1007_s10957-006-9103-y
    DOI: 10.1007/s10957-006-9103-y
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    References listed on IDEAS

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    1. A. Guerraggio & D. T. Luc, 2001. "Optimality Conditions for C1,1 Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 615-629, June.
    2. A. Guerraggio & D.T. Luc, 2003. "Optimality Conditions for C 1,1 Constrained Multiobjective Problems," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 117-129, January.
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    Cited by:

    1. P. Q. Khanh & N. D. Tuan, 2007. "Optimality Conditions for Nonsmooth Multiobjective Optimization Using Hadamard Directional Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 341-357, June.
    2. C. Gutiérrez & B. Jiménez & V. Novo, 2009. "New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 85-106, July.
    3. Ram U. Verma & G. J. Zalmai, 2018. "Parameter-free duality models and applications to semiinfinite minmax fractional programming based on second-order ( $$\phi ,\eta ,\rho ,\theta ,{\tilde{m}}$$ ϕ , η , ρ , θ , m ~ )-sonvexities," OPSEARCH, Springer;Operational Research Society of India, vol. 55(2), pages 381-410, June.
    4. P. Q. Khanh & L. T. Tung, 2012. "Local Uniqueness of Solutions to Ky Fan Vector Inequalities using Approximations as Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 840-854, December.
    5. Khanh, Phan Quoc & Quyen, Ho Thuc & Yao, Jen-Chih, 2011. "Optimality conditions under relaxed quasiconvexity assumptions using star and adjusted subdifferentials," European Journal of Operational Research, Elsevier, vol. 212(2), pages 235-241, July.
    6. P. Khanh & L. Tung, 2015. "First- and second-order optimality conditions for multiobjective fractional programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 419-440, July.

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