Variant Gradient Projection Methods for the Minimization Problems

Selection Strategies in Projection Methods for Convex Minimization Problems

We propose new projection method for nonsmooth convex minimization problems. We present some method of subgradient selection, which is based on the so called residual selection model and is a generalization of the so called obtuse cone model. We also present numerical results for some test problems and compare these results with some other convex nonsmooth minimization methods. The numerical re...

Alternating minimization and projection methods for structured nonconvex problems

We study the convergence properties of an alternating proximal minimization algorithm for nonconvex structured functions of the type: L(x, y) = f(x)+Q(x, y)+g(y), where f : R → R∪{+∞} and g : R → R∪{+∞} are proper lower semicontinuous functions, and Q : R × R → R is a smooth C function which couples the variables x and y. The algorithm can be viewed as a proximal regularization of the usual Gau...

Regularized gradient-projection methods for finding the minimum-norm solution of the constrained convex minimization problem

Let H be a real Hilbert space and C be a nonempty closed convex subset of H. Assume that g is a real-valued convex function and the gradient ∇g is [Formula: see text]-ism with [Formula: see text]. Let [Formula: see text], [Formula: see text]. We prove that the sequence [Formula: see text] generated by the iterative algorithm [Formula: see text], [Formula: see text] converges strongly to [Formul...

A Regularized Gradient Projection Method for the Minimization Problem

Strong convergence of modified gradient-projection algorithm for constrained convex minimization problems

In this article, a modified gradient-projection algorithm (GPA) is introduced, which combines Xu’s idea of an alternative averaged mapping approach to the GPA and the general iterative method for nonexpansive mappings in Hilbert space introduced by Marino and Xu. Under suitable conditions, it is proved that the strong convergence of the sequences generated by implicit and explicit schemes to a ...