Second, the sub-problem is solved by an adaptive regularization gradient projection method, characterized by an iterate-varying hyper-ellipsoidal based norm.
A hyper-ellipsoids regularization gradient projection method 1.
We directly see that this iteration coincides with the generalized gradient projection method if [lambda] is identified with [1/[lambda].
Let us note that the inner iterations also need an evaluation of K', hence their numerical costs is of the same order as an iteration step of the conditional gradient projection method.
A family of clustering criteria is introduced, and an alternating optimization algorithm is developed by adapting a gradient projection method
to fit each variant of the fuzzy clustering model.
The gradient projection method has many of the same properties as the steepest descent method, including a slow convergence rate.
BERTSEKAS, On the Goldstein-Levitin-Poljak Gradient Projection Method, IEEE Transactions on Automatic Control, 21 (1976), pp.
Recently, similar techniques were tactfully managed to different traditional algorithms [8,10,11,16,17] andcorresponding optimal complexity results were obtained: Beck and Teboulle  proposed a fast duality-based gradient projection methods
to solve TV; Chambolle and Pock  and Goldfarb et al.