Subgradient algorithms for solving variable inequalities

In this paper we consider the variable inequalities problem, that is, to find a solution of the inclusion given by the sum of a function and a point-to-cone application. This problem can be seen as a generalization of the classical inequalities problem taking a variable order structure. Exploiting this relation, we propose two variants of the subgradient algorithm for solving the variable inequalities model. The convergence analysis is given under convex-like conditions, which, when the point-to-cone application is constant, contains the old subgradient schemes.