Mond–Weir Duality and Optimality for Nonsmooth Vector Bilevel Programs in Terms of Approximations

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Document Type : Original paper

Authors

1 Department of Mathematics, National Institute of Technology Mizoram, Aizawl, 796012, Mizoram, India

2 Department of Mathematics, Satish Chandra College, Ballia, India

Abstract

This paper addresses a nonsmooth vector bilevel optimization problem. By reformulating the hierarchical model into a single-level problem using the optimal value approach, we establish sufficient optimal- ity conditions for the nonsmooth extremum problem. These conditions rely on the assumption that the functions involved exhibit generalized convexity, characterized through their approximations. Additionally, we introduce Mond–Weir-type dual models for these problems and prove several duality theorems within the generalized convexity frame- work. The applicability of these optimality conditions is demonstrated through illustrative examples of nonsmooth vector bilevel optimization problems.

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References

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Communications in Combinatorics and Optimization

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Available Online from 27 June 2026

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