A Subgradient-Like Algorithm for Solving Vector Convex Inequalities

In this paper, we propose a strongly convergent variant of Robinson’s subgradient algorithm for solving a system of vector convex inequalities in Hilbert spaces. The advantage of the proposed method is that it converges strongly, when the problem has solutions, under mild assumptions. The proposed algorithm also has the following desirable property: the sequence converges to the solution of the problem, which lies closest to the starting point, and remains entirely in the intersection of three balls with radius less than the initial distance to the solution set.