A class of methods for solving large convex systems

A class of methods for solving a large system of convex inequalities is given. All of the methods in the class rely on the technique of solving a large convex system by iteratively solving systems with a smaller number of inequalities. It is shown that the method due to Agmon for solving a system of linear inequalities belongs to this class. The simultaneous projection, and the aggregation algorithms are new methods that also belong to this class.