Delayed Star Subgradient Methods for Constrained Nondifferentiable Quasi-Convex Optimization

In this work, we consider the problem of minimizing a quasi-convex function over a nonempty closed convex constrained set. In order to approximate a solution of the considered problem, we propose delayed star subgradient methods. The main feature of the proposed methods is that it allows us to use the stale star subgradients when updating the next iteration rather than computing the new star subgradient in every iteration. We subsequently investigate the convergence results of sequences generated by the proposed methods. Finally, we present some numerical experiments on the Cobb–Douglas production efficiency problem to illustrate the effectiveness of the proposed method.