A Nonmonotone Smoothing-Type Algorithm for a System of Inequalities Associated with Circular Cones

This is the authors' abstract. We don't add key points for this paper.

In this paper, we consider a system of inequalities associated with circular cones. By constructing a new smoothing function, the problem is reformulated as a system of parameterized smooth equations. In addition, we suggest a Newton-type algorithm for solving the smooth equations so that a solution of the problem concerned is found. In particular, the algorithm is proved to be globally and locally quadratically convergent under suitable conditions. The preliminary numerical results demonstrate that the algorithm is effective.