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Solving nonsmooth interval optimization problems based on interval-valued symmetric invexity

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  • Guo, Yating
  • Ye, Guoju
  • Liu, Wei
  • Zhao, Dafang
  • Treanţǎ, Savin

Abstract

This paper focuses on a nonsmooth nonconvex interval-valued optimization problem. For this, we propose interval-valued symmetric invexity, interval-valued symmetric pseudo-invexity and interval-valued symmetric quasi-invexity in terms of the symmetric gH-differentiable interval-valued functions. Some important properties of these generalized convexities are also discussed. By utilizing these new concepts, we establish sufficient Karush–Kuhn–Tucker conditions for the considered problem. Further, the Wolfe and Mond–Weir type dual problems are associated and weak, strong and strict converse duality results have been derived. Finally, we apply the developed theory to a binary classification problem of interval data by support vector machine.

Suggested Citation

  • Guo, Yating & Ye, Guoju & Liu, Wei & Zhao, Dafang & Treanţǎ, Savin, 2023. "Solving nonsmooth interval optimization problems based on interval-valued symmetric invexity," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s096007792300735x
    DOI: 10.1016/j.chaos.2023.113834
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    References listed on IDEAS

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    1. Yating Guo & Guoju Ye & Wei Liu & Dafang Zhao & Savin Treanţǎ, 2021. "Optimality Conditions and Duality for a Class of Generalized Convex Interval-Valued Optimization Problems," Mathematics, MDPI, vol. 9(22), pages 1-14, November.
    2. Singh, D. & Dar, B.A. & Kim, D.S., 2016. "KKT optimality conditions in interval valued multiobjective programming with generalized differentiable functions," European Journal of Operational Research, Elsevier, vol. 254(1), pages 29-39.
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    6. Guo, Yating & Ye, Guoju & Liu, Wei & Zhao, Dafang & Treanţă, Savin, 2022. "On symmetric gH-derivative: Applications to dual interval-valued optimization problems," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    7. Zhang, Chenglong & Guo, Ping & Huo, Zailin, 2021. "Irrigation water resources management under uncertainty: An interval nonlinear double-sided fuzzy chance-constrained programming approach," Agricultural Water Management, Elsevier, vol. 245(C).
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    9. Tian, Yuan & Li, Chunxue & Liu, Jing, 2023. "Complex dynamics and optimal harvesting strategy of competitive harvesting models with interval-valued imprecise parameters," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    10. Sharifi, Mani & Taghipour, Sharareh & Abhari, Abdolreza, 2021. "Inspection interval optimization for a k-out-of-n load sharing system under a hybrid mixed redundancy strategy," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
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