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

doi:10.1007/s40305-022-00423-7

Journal of the Operations Research Society of China ›› 2023, Vol. 11 ›› Issue (4): 809-826.doi: 10.1007/s40305-022-00423-7

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

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

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

Received:2021-01-25 Revised:2022-03-03 Online:2023-12-30 Published:2023-12-26
Contact: Guo-Lin Yu, Xiao Pan, Tian-Tian Gong E-mail:guolin_yu@126.com;970525882@qq.com;1965447108@qq.com
Supported by:
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).

Abstract

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.

Key words: Multi-objective fractional programming, Robust weak efficient solution, Generalized convex function, Optimality condition, Saddle point

CLC Number:

Xiao Pan, Guo-Lin Yu, Tian-Tian Gong. Optimality Conditions for Generalized Convex Nonsmooth Uncertain Multi-objective Fractional Programming[J]. Journal of the Operations Research Society of China, 2023, 11(4): 809-826.

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References

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

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