It is well known that under the Wolfe–Powell inexact line search, global convergence of nonlinear conjugate gradient method always requires Lipschitz continuous condition for nonconvex functions. In this paper, we find unnecessary proving particular algorithms if its searching direction has well-known sufficient descent property and trust region feature. Thus, family proposed by Yuan et al. (Nu...

The iterative aggregation method for the solution of linear systems is extended in several directions: to operators on Banach spaces; to the method with inexact correction, i.e., to methods where the (inner) linear system is in turn solved iteratively; and to the problem of nding stationary distributions of Markov operators. Local convergence is shown in all cases. Convergence results apply to ...

We extend the general decomposition scheme of [32], which is based on the hybrid inexact proximal point method of [38], to allow the use of variable metric in subproblems, along the lines of [23]. We show that the new general scheme includes as special cases the splitting method for composite mappings [25] and the proximal alternating directions method [13, 17] (in addition to the decomposition...

We present a line-search algorithm for large-scale continuous optimization. The algorithm is matrix-free in that it does not require the factorization of derivative matrices. Instead, it uses iterative linear system solvers. Inexact step computations are supported in order to save computational expense during each iteration. The algorithm is an interior-point approach derived from an inexact Ne...

Users might use general terms to query the information in need, when the exact keyword is unknown. We treat these inexact query terms as general queries. In this paper, we consturct a test data set to evaluate the performance of online search engine on searching Wikipedia with general queries and exact queries. We also proposed a new query expansion method that performs better on general querie...

Sparse covariance selection problems can be formulated as log-determinant (log-det ) semidefinite programming (SDP) problems with large numbers of linear constraints. Standard primal-dual interior-point methods that are based on solving the Schur complement equation would encounter severe computational bottlenecks if they are applied to solve these SDPs. In this paper, we consider a customized ...

In this paper a new approach to exact and inexact graph matching is introduced. We propose a compact network representation for graphs, which is capable of sharing identical subgraphs of one or several model graphs. The new matching algorithm NA works on the network and uses its compactness in order to speed up the detection process. Next, the problem of inexact graph matching is described and ...

In this paper we describe a variant of the Inexact Newton method for solving nonlinear systems of equations. We define a nonmonotone Inexact Newton step and a nonmonotone backtracking strategy. For this nonmonotone Inexact Newton scheme we present the convergence theorems. Finally, we show how we can apply these strategies to Inexact Newton Interior–Point method and we present some numerical ex...

We present an incremental joint framework to simultaneously extract entity mentions and relations using structured perceptron with efficient beam-search. A segment-based decoder based on the idea of semi-Markov chain is adopted to the new framework as opposed to traditional token-based tagging. In addition, by virtue of the inexact search, we developed a number of new and effective global featu...