Robust optimality and duality for bilevel optimization problems under uncertain data

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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, 277001, Uttar Pradesh, India

Abstract

The exploration of robust bilevel programming problems is a relatively new development in optimization theory. In this study, we examine a bilevel optimization problem in which both the upper-level and lower-level constraints involve uncertainty. By reducing the problem to a single-level, nonlinear and non-smooth program, we explore sufficient optimality conditions and duality theorems for robust optimal solutions of the considered non-smooth uncertain bilevel optimization problem, using Clarke subdifferentials. Leveraging the characteristics of Clarke subdifferentials, we propose Wolfe-type robust dual models. Additionally, we establish various duality theorems, including weak and strong robust duality, in terms of Clarke subdifferentials. Several illustrative examples are presented to confirm the applicability of the results developed.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 20 March 2025

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