Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.9.2025.4.04

Volume 9, Issue 4, 1 August 2025, Pages 523-538

 

Abstract. This paper presents a novel variant of the Broyden quasi-Newton secant-type method aimed at solving constrained mixed generalized equations, which can include functions that are not necessarily differentiable. The proposed method integrates the classical secant approach with techniques inspired by the Conditional Gradient method to handle constraints effectively. We establish local convergence results by applying the contraction mapping principle. Specifically, under assumptions of Lipschitz continuity, a modified Broyden update for derivative approximation, and the metric regularity property, we show that the algorithm generates a well-defined sequence that converges locally at a Q-linear rate.

 

How to Cite this Article:
P. C. da Silva Junior, O. P. Ferreira, G. N. Silva, Broyden quasi-Newton secant-type method for solving constrained mixed generalized equations, J. Nonlinear Var. Anal. 9 (2025), 523-538.