Generalized Sor-Like Iteration Methods for Absolute Value Equations Associated With Circular Cones

In this paper, we study the absolute value equations associated with circular cones (referred to as CCAVE). The circular cone is a type of non-symmetric cone that generalizes the second-order cone. By equivalently reformulating CCAVE as a two-by-two block nonlinear equation, we propose a class of generalized SOR-like iteration methods for solving CCAVE. Useful properties of the circular cone are explored, and sufficient conditions for ensuring the convergence of the generalized SOR-like iteration methods are analyzed. Numerical experiments demonstrate the effectiveness of the proposed methods in solving CCAVE.