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Optimality Conditions for Generalized Convex Nonsmooth Uncertain Multi-objective Fractional Programming

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Abstract

This paper aims at studying optimality conditions of robust weak efficient solutions for a nonsmooth uncertain multi-objective fractional programming problem (NUMFP). The concepts of two types of generalized convex function pairs, called type-I functions and pseudo-quasi-type-I functions, are introduced in this paper for (NUMFP). Under the assumption that (NUMFP) satisfies the robust constraint qualification with respect to Clarke subdifferential, necessary optimality conditions of the robust weak efficient solution are given. Sufficient optimality conditions are obtained under pseudo-quasi-type-I generalized convexity assumption. Furthermore, we introduce the concept of robust weak saddle points to (NUMFP), and prove two theorems about robust weak saddle points. The main results in the present paper are verified by concrete examples.

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Authors and Affiliations

  1. School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, Ningxia, China

    Xiao Pan, Guo-Lin Yu & Tian-Tian Gong

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  1. Xiao Pan
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  2. Guo-Lin Yu
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  3. Tian-Tian Gong
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All authors contributed to the study conception and design of this paper.

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Correspondence to Guo-Lin Yu.

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The authors contributed equally to this paper, and we declare that we have no conflict of interest.

Additional information

This research was supported by Natural Science Foundation of China (Nos. 11861002 and 12171601), the Key Project of North Minzu University (No. ZDZX201804), the Construction Project of First-Class Disciplines in Ningxia Higher Education (NXYLXK2017B09), the Postgraduate Innovation Project of North Minzu Universit (No. YCX21157). .

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Pan, X., Yu, GL. & Gong, TT. Optimality Conditions for Generalized Convex Nonsmooth Uncertain Multi-objective Fractional Programming. J. Oper. Res. Soc. China 11, 809–826 (2023). https://doi.org/10.1007/s40305-022-00423-7

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  • DOI: https://doi.org/10.1007/s40305-022-00423-7

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