Preprint D103/2013
A Subgradient-like Algorithm for Solving Vector Convex Inequalities

L.R. Lucambio Pérez | Bello Cruz, J.Y.

**Keywords: **
Projection methods · Strong convergence · Subgradient algorithm · Vector convex functions

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.