Optimality and duality in nonsmooth multiobjective fractional programming problem with constraints

Tran Su () and Dinh Dieu Hang ()
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Tran Su: Quang Nam University
Dinh Dieu Hang: Thai Nguyen University of Information and Communication Technology

4OR, 2022, vol. 20, issue 1, No 5, 105-137

Abstract: Abstract In this paper, we establish some quotient calculus rules in terms of contingent derivatives for the two extended-real-valued functions defined on a Banach space and study a nonsmooth multiobjective fractional programming problem with set, generalized inequality and equality constraints. We define a new parametric problem associated with these problem and introduce some concepts for the (local) weak minimizers to such problems. Some primal and dual necessary optimality conditions in terms of contingent derivatives for the local weak minimizers are provided. Under suitable assumptions, sufficient optimality conditions for the local weak minimizers which are very close to necessary optimality conditions are obtained. An application of the result for establishing three parametric, Mond–Weir and Wolfe dual problems and several various duality theorems for the same is presented. Some examples are also given for our findings.

Keywords: Nonsmooth multiobjective fractional programming problem with constraints; Optimality conditions; Duality; Weak minimizers; Contingent derivatives; 90C32; 90C29; 49K99 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10288-020-00470-x

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