New smoothing functions for solving a system of equalities and inequalities (Q2789167)

A family of smoothing functions for solving a system of equations and inequalities that generalizes the one introduced in [\textit{Y. Zhang} and \textit{Z.-H. Huang}, J. Comput. Appl. Math. 233, No. 9, 2312--2321 (2010; Zbl 1181.90265)] is proposed. A corresponding nonmonotone smoothing type algorithm is provided and investigated, being based on a new reformation \(\hat H\) but with less dimensionality, its local and global convergence, respectively, being proven under suitable assumptions. Moreover, it is shown through concrete numerical examples that some unsolved examples from the mentioned paper can be solved by a newly proposed method. An interesting feature of the new algorithm is that the involved parameters in the family of new smoothing functions do not influence the convergence of the algorithm.