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The KKT optimality conditions in a class of generalized convex optimization problems with an interval-valued objective function

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Abstract

In this paper, we study the Karush–Kuhn–Tucker optimality conditions in a class of nonconvex optimization problems with an interval-valued objective function. Firstly, the concepts of preinvexity and invexity are extended to interval-valued functions. Secondly, several properties of interval-valued preinvex and invex functions are investigated. Thirdly, the KKT optimality conditions are derived for LU-preinvex and invex optimization problems with an interval-valued objective function under the conditions of weakly continuous differentiablity and Hukuhara differentiablity. Finally, the relationships between a class of variational-like inequalities and the interval-valued optimization problems are established.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No.60974082), and the Science Plan Foundation of the Education Bureau of Shaanxi Province (Nos. 11JK1051, 2010JK835).

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Xidian University, Xi’an, China

    Jianke Zhang, Sanyang Liu, Lifeng Li & Quanxi Feng

  2. Department of Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, China

    Jianke Zhang

  3. School of Science, Guilin University of Technology, Guilin, China

    Quanxi Feng

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  1. Jianke Zhang
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  2. Sanyang Liu
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  3. Lifeng Li
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  4. Quanxi Feng
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Correspondence to Jianke Zhang.

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Zhang, J., Liu, S., Li, L. et al. The KKT optimality conditions in a class of generalized convex optimization problems with an interval-valued objective function. Optim Lett 8, 607–631 (2014). https://doi.org/10.1007/s11590-012-0601-6

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  • DOI: https://doi.org/10.1007/s11590-012-0601-6

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