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Second-order strong optimality and duality for nonsmooth multiobjective fractional programming with constraints

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Abstract

This paper investigates nonsmooth multiobjective fractional programming (NMFP) with inequalities and equalities constraints in real reflexive Banach spaces. It derives a quotient calculus rule for computing the first- and second-order Clarke derivatives of fractional functions involving locally Lipschitz functions. A novel second-order Abadie-type regularity condition is presented, defined with the help of the Clarke directional derivative and the Páles–Zeidan second-order directional derivative. We establish both first- and second-order strong necessary optimality conditions, which contain some new information on multipliers and imply the strong KKT necessary conditions, for a Borwein-type properly efficient solution of NMFP by utilizing generalized directional derivatives. Moreover, it derives second-order sufficient optimality conditions for NMFP under a second-order generalized convexity assumption. Additionally, we derive duality results between NMFP and its second-order dual problem under some appropriate conditions

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Acknowledgements

The authors would like to express their sincere thanks to the associated editor and anonymous referees for valuable comments and providing nice references [6,7,8,9,10]. This paper was supported by the Natural Science Foundation of China (Nos. 12071379, 12271061), the Natural Science Foundation of Chongqing(cstc2021jcyj-msxmX0925, cstc2022ycjh-bgzxm0097), Youth Project of Science and Technology Research Program of Chongqing Education Commission of China (No. KJQN202201802) and the Southwest University Graduate Research Innovation Program (No. SWUS23058). D. Ghosh is thankful for the research funding CRG (CRG/2022/001347) and MATRICS (MTR/2021 /000696), SERB, India. J.-C. Yao acknowledges MOST (No. 111-2115-M-039-001-MY2), Taiwan.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    Jiawei Chen & Luyu Liu

  2. School of Information and Mathematics, Yangtze University, Jingzhou, 434023, China

    Yibing Lv

  3. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, 221005, India

    Debdas Ghosh

  4. Research Center for Interneural Computing, China Medical University, Taichung, 40447, Taiwan

    Jen Chih Yao

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  1. Jiawei Chen
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  2. Luyu Liu
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Contributions

Jiawei Chen and Luyu Liu wrote the main manuscript text, Yibing Lv and Debdas Ghosh revised the manuscript text and Jen-Chih Yao gave the idea of the manscript and suggestions. All authors reviewed the manuscript.

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Correspondence to Jiawei Chen.

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Chen, J., Liu, L., Lv, Y. et al. Second-order strong optimality and duality for nonsmooth multiobjective fractional programming with constraints. Positivity 28, 36 (2024). https://doi.org/10.1007/s11117-024-01052-5

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