SUPERIORIZATION WITH A PROJECTED SUBGRADIENT METHOD

In this paper, we study a constrained minimization problem with a convex objective function and a feasible region, which is the intersection of finitely many closed convex constraint sets. We use a projected subgradient method combined with a dynamic string-averaging projection method with variable strings and variable weights, as a feasibility-seeking algorithm. It is shown that any sequence, generated by the superiorized version of a dynamic string-averaging projection algorithm, not only converges to a feasible point but, additionally, also either its limit point solves the constrained minimization problem or the sequence is strictly Fejér monotone with respect to the solution set. © 2022 Journal of Applied and Numerical Optimization.