Robust optimality and duality relations for multiobjective semi-infinite equilibrium problems having vanishing constraints with uncertain data

This article investigates a multiobjective semi-infinite equilibrium problem having vanishing constraints with uncertain data. Such models frequently arise in engineering design, economics, and decision-making under uncertainty. Using the VC-Abadie constraint qualification, we first establish the necessary optimality condition, followed by a sufficient optimality result for the proposed model under the generalized convexity framework. Additionally, we formulate robust Wolfe and robust Mond-Weir type dual models for the considered multiobjective semi-infinite equilibrium problems and derive the usual robust duality results between the considered problem and the dual models under the generalized convexity assumptions. Furthermore, the discussed theoretical results are validated through various non-trivial numerical examples. Moreover, an application of the proposed model to a multiobjective transportation problem is presented. This further illustrates the practical advantages of employing the considered dual models and emphasizes the significance of the corresponding duality relations.