A Non-Monotone Smoothing Newton Algorithm for Solving the System of Generalized Absolute Value Equations (Journal of Computational Mathematics, 2024)
The system of generalized absolute value equations (GAVE) has attracted more andmore attention in the optimization community. In this paper, by introducing a smoothingfunction, we develop a smoothing Newton algorithm with non-monotone line search to solvethe GAVE. We show that the non-monotone algorithm is globally and locally quadraticallyconvergent under a weaker assumption than those given in most existing algorithms forsolving the GAVE. Numerical results are given to demonstrate the viability and efficiencyof the approach.