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The system of generalized absolute value equations (GAVE) has attracted moreand more attention in the optimization community. In this paper, by introducinga smoothing function, we develop a smoothing Newton algorithm with non-monotoneline search to solve the GAVE. We show that the non-monotone algorithm isglobally and locally quadratically convergent under a weaker assumption thanthose given in most existing algorithms for solving the GAVE. Numerical resultsare given to demonstrate the viability and efficiency of the approach.

A non-monotone smoothing Newton algorithm for solving the system of generalized absolute value equations