V sequence fxkg. Similar result is also true for quasiNewton methods with trust region (see [16]). Another type of special quasi-Newton methods is that the quasi-Newton matrices are sparse. It is quite often that large-scale problems have separable structure, which leads to special structure of the Hessian matrices. In such cases we can require the quasiNewton matrices to have similar structures.

In this paper, non-monotone line search procedure is studied, which is combined with the non-quasi-Newton family. Under the uniformly convexity assumption on objective function, the global and superlinear convergence of the non-quasi-Newton family with the proposed nonmonotone line search is proved under suitable conditions.

We investigate some basic descriptive set theory for countably based completely quasi-metrizable topological spaces, which we refer to as quasi-Polish spaces. These spaces naturally generalize much of the classical descriptive set theory of Polish spaces to the non-Hausdorff setting. We show that a subspace of a quasi-Polish space is quasi-Polish if and only if it is Π2 in the Borel hierarchy. ...

In this report, we propose a new partitioned variable metric method for minimizing nonsmooth partially separable functions. After a short introduction, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Computational experiments given confirm efficiency and robustness of the new met...

‎the notion of quasi-einstein metric in physics is equivalent to the notion of ricci soliton in riemannian spaces‎. ‎quasi-einstein metrics serve also as solution to the ricci flow equation‎. ‎here‎, ‎the riemannian metric is replaced by a hessian matrix derived from a finsler structure and a quasi-einstein finsler metric is defined‎. ‎in compact case‎, ‎it is proved that the quasi-einstein met...

Ensemble learning with output from multiple supervised and unsupervised models aims to improve the classification accuracy of supervised model ensemble by jointly considering the grouping results from unsupervised models. In this paper we cast this ensemble task as an unconstrained probabilistic embedding problem. Specifically, we assume both objects and classes/clusters have latent coordinates...

It was shown in a previous work that some blind methods can be made robust to channel order overmodeling by using the l1 or lp quasi-norms. However, no theoretical argument has been provided to support this statement. In this work, we study the robustness of subspace blind based methods using l1 or lp quasi-norms. For the l1 norm, we provide the sufficient and necessary condition that the chann...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus, every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fai...