Sufficiency and duality of multi-objective bi-level programming problem under Guignard constraint qualification.

Although a great deal of work has been done on bi-level programming problems (BPPs) during the last few decades, there is still a substantial gap in the literature on sufficient optimality conditions and duality results of BPPs. This article aims to develop sufficient optimality conditions and Mond-Weir-type dual for a multi-objective BPP from an optimistic perspective under the Guignard constraint qualification. Using the weighted sum scalarisation at the lower level and a special function at the upper level, we convert the multi-objective BPP to the corresponding single-objective BPP. With the help of optimal value reformulation, we reformulate the single-objective BPP as a single-level mathematical programming problem. Using the generalised convexity, we develop sufficient optimality conditions. Moreover, we formulate Mond-Weir type dual and establish the corresponding duality results. [ABSTRACT FROM AUTHOR]