In this paper, we focus on the local convergence analysis of an inexact quasi-Newton method for solving generalized equations in Euclidean space. To deal with the problem of calculate the derivative in each step of our proposed method, we substitute \(f'(\cdot )\) with a sequence \(\{B_k\}\) which satisfies the classical bounded deterioration condition. In particular, we demonstrate the linear and superlinear convergence of our algorithm using the Broyden update. Moreover, we propose that the subproblem to be solved in each iteration can be computed inexactly. As a consequence, this paper extends several important results in the literature. Lastly, but no less importantly, our proposed convergence results are derived using a new metric regularity assumption on the multifunction that governs the main problem. This assumption was first analyzed in Adly et al. (Journal of Mathematical Analysis and Applications, 439(1):396–418, 2016), but it was never been studied in the context of the inexact quasi-Newton method with Broyden update.
