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April 16, 2026Open Access

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

Key Points

The research aims to address absolute value equations associated with circular cones and develop effective solution methods.
Reformulated absolute value equations as a two-by-two block nonlinear equation
Proposed a class of generalized SOR-like iteration methods
Analyzed sufficient conditions for convergence
Conducted numerical experiments to validate effectiveness
Proposed methods successfully solve absolute value equations associated with circular cones
Demonstrated improvements in convergence rates in numerical experiments
Highlighted properties of circular cones that enhance method effectiveness

Abstract

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.

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