We propose new versions of accelerated first order methods for convex composite optimization, where the prox parameter is allowed to increase from one iteration to the next. In particular we show that a full backtracking strategy can be used within the FISTA [1] and FALM algorithms [7] while preserving their worst-case iteration complexities of O( √ L(f)/ ). In the original versions of FISTA an...

Newton’s method for the inverse matrix pth root, A−1/p, has the attraction that it involves only matrix multiplication. We show that if the starting matrix is cI for c ∈ R then the iteration converges quadratically to A−1/p if the eigenvalues of A lie in a wedge-shaped convex set containing the disc { z : |z−cp| < cp }. We derive an optimal choice of c for the case where A has real, positive ei...

In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly nonseparable or ill conditioned problems. We call the method Flexible Coordinate Descent (FCD). At each iterat...

We first propose an adaptive accelerated proximal gradient (APG) method for minimizing strongly convex composite functions with unknown convexity parameters. This method incorporates a restarting scheme to automatically estimate the strong convexity parameter and achieves a nearly optimal iteration complexity. Then we consider the l1regularized least-squares (l1-LS) problem in the high-dimensio...

We employ a variant of the popular Adaboost algorithm to train multiple acoustic models such that the aggregate system exhibits improved performance over the individual recognizers. Each model is trained sequentially on re-weighted versions of the training data. At each iteration, the weights are decreased for the frames that are correctly decoded by the current system. These weights are then m...

Rule Definition: Primitive events are principally entity manipulation events generated by operations such as creations, deletions, access, updates (of an entity or a part of it), changes of the persistency status, insertions and deletions into/from collections and method calls. The moment of generation(i.e., when an event occurs) can be either before or after the actual operation depending on t...

We present an improved version of a full Nesterov-Todd step infeasible interior-point method for linear complementarityproblem over symmetric cone (Bull. Iranian Math. Soc., 40(3), 541-564, (2014)). In the earlier version, each iteration consisted of one so-called feasibility step and a few -at most three - centering steps. Here, each iteration consists of only a feasibility step. Thus, the new...

In the present paper, we show that $S^*$ iteration method can be used to approximate fixed point of almost contraction mappings. Furthermore, we prove that this iteration method is equivalent to CR iteration method  and it produces a slow convergence rate compared to the CR iteration method for the class of almost contraction mappings. We also present table and graphic to support this result. F...