1,720,999 research outputs found
On the Convergence Properties of a Stochastic Trust-Region Method with Inexact Restoration
Full text linkWe study the convergence properties of SIRTR, a stochastic inexact restoration trust-region method suited for the minimization of a finite sum of continuously differentiable functions. This method combines the trust-region methodology with random function and gradient estimates formed by subsampling. Unlike other existing schemes, it forces the decrease of a merit function by combining the function approximation with an infeasibility term, the latter of which measures the distance of the current sample size from its maximum value. In a previous work, the expected iteration complexity to satisfy an approximate first-order optimality condition was given. Here, we elaborate on the convergence analysis of SIRTR and prove its convergence in probability under suitable accuracy requirements on random function and gradient estimates. Furthermore, we report the numerical results obtained on some nonconvex classification test problems, discussing the impact of the probabilistic requirements on the selection of the sample sizes
Approximate norm descent methods for constrained nonlinear systems
Full text linkWe address the solution of convex-constrained nonlinear systems of equations where the Jacobian matrix is unavailable or its computation/ storage is burdensome. In order to efficiently solve such problems, we propose a new class of algorithms which are "derivative-free" both in the computation of the search direction and in the selection of the steplength. Search directions comprise the residuals and quasi-Newton directions while the steplength is determined by using a new linesearch strategy based on a nonmonotone approximate norm descent property of the merit function. We provide a theoretical analysis of the proposed algorithm and we discuss several conditions ensuring convergence to a solution of the constrained nonlinear system. Finally, we illustrate its numerical behaviour also in comparison with existing approaches
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
On the use of iterative methods in cubic regularization for unconstrained optimization
No full textIn this paper we consider the problem of minimizing a smooth function by using the adaptive cubic regularized (ARC) framework. We focus on the computation of the trial step as a suitable approximate minimizer of the cubic model and discuss the use of matrix-free iterative methods. Our approach is alternative to the implementation proposed in the original version of ARC, involving a linear algebra phase, but preserves the same worst-case complexity count. Further we introduce a new stopping criterion in order to properly manage the “over-solving” issue arising whenever the cubic model is not an adequate model of the true objective function. Numerical experiments conducted by using a nonmonotone gradient method as inexact solver are presented. The obtained results clearly show the effectiveness of the new variant of ARC algorithm
On preconditioner updates for sequences of saddle-point linear systems
No full textUpdating preconditioners for the solution of sequences of large and sparse saddlepoint
linear systems via Krylov methods has received increasing attention in the last few
years, because it allows to reduce the cost of preconditioning while keeping the efficiency
of the overall solution process. This paper provides a short survey of the two approaches
proposed in the literature for this problem: updating the factors of a preconditioner
available in a block LDL' form, and updating a preconditioner via a limited-memory
technique inspired by quasi-Newton methods
On the update of constraint preconditioners for regularized KKT systems
No full textWe address the problem of preconditioning sequences of regularized KKT systems, such as those arising in interior point methods for convex quadratic programming. In this case, constraint preconditioners (CPs) are very effective and widely used; however, when solving large-scale problems, the computational cost for their factorization may be high, and techniques for approximating them appear as a convenient alternative. Here, given a block LDLT factorization of the CP associated with a KKT matrix of the sequence, called seed matrix, we present a technique for updating the factorization and building inexact CPs for subsequent matrices of the sequence. We have recently proposed an updating procedure that performs a low-rank correction of the Schur complement of the (1,1) block of the CP for the seed matrix. Now we focus on KKT sequences with nonzero (2,2) blocks and make a step further, by enriching the low-rank correction of the Schur complement by an additional cheap update. The latter update takes into account information not included in the former one and expressed as a diagonal modification of the low-rank correction. Theoretical results and numerical experiments show that the new strategy can be more effective than the procedure based on the low-rank modification alone
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