1,720,982 research outputs found
Introduction to Methods for Nonlinear Optimization
No full textThis book has two main objectives:
• to provide a concise introduction to nonlinear optimization methods, which can be used as a textbook at a graduate or upper undergraduate level;
• to collect and organize selected important topics on optimization algorithms, not easily found in textbooks, which can provide material for advanced courses or can serve as a reference text for self-study and research.
The basic material on unconstrained and constrained optimization is organized into two blocks of chapters:
• basic theory and optimality conditions
• unconstrained and constrained algorithms.
These topics are treated in short chapters that contain the most important results in theory and algorithms, in a way that, in the authors’ experience, is suitable for introductory courses.
A third block of chapters addresses methods that are of increasing interest for solving difficult optimization problems. Difficulty can be typically due to the high nonlinearity of the objective function, ill-conditioning of the Hessian matrix, lack of information on first-order derivatives, the need to solve large-scale problems.
In the book various key subjects are addressed, including: exact penalty functions and exact augmented Lagrangian functions, non monotone methods, decomposition algorithms, derivative free methods for nonlinear equations and optimization problems.
The appendices at the end of the book offer a review of the essential mathematical background, including an introduction to convex analysis that can make part of an introductory course
Decomposition Techniques for Multilayer Perceptron Training
No full textIn this paper, we consider the learning problem of multilayer perceptrons (MLPs) formulated as the problem of minimizing a smooth error function. As well known, the learning problem of MLPs can be a difficult nonlinear nonconvex optimization problem. Typical difficulties can be the presence of extensive flat regions and steep sided valleys in the error surface, and the possible large number of training data and of free network parameters. We define a wide class of batch learning algorithms for MLP, based on the use of block decomposition techniques in the minimization of the error function. The learning problem is decomposed into a sequence of smaller and structured minimization problems in order to advantageously exploit the structure of the objective function. Theoretical convergence results are established, and a specific algorithm is constructed and evaluated through an extensive numerical experimentation. The comparisons with the state-of-the-art learning algorithms show the effectiveness of the proposed techniques
An unconstrained minimization method for solving low rank SDP relaxations of the max cut problem
No full textIn this paper we consider low-rank semidefinite programming (LRSDP)
relaxations of combinatorial quadratic problems that are equivalent to the maxcut
problem. Using the Gramian representation of a positive semidefinite matrix, the
LRSDP problem can be formulated as the nonconvex nonlinear programming prob-
lem of minimizing a quadratic function with quadratic equality constraints. For the
solution of this problem we propose a continuously differentiable exact merit func-
tion that exploits the special structure of the constraints and we use this function to
define an efficient and globally convergent algorithm. Finally, we test our code on an
extended set of instances of the maxcut problem and we report comparisons with other
existing codes
Necessary and sufficient global optimality conditions for NLP reformulations of linear SDP problems
No full textIn this paper we consider the standard linear SDP problem, and its low rank
nonlinear programming reformulation, based on a Gramian representation of a positive semi-
definite matrix. For this nonconvex quadratic problem with quadratic equality constraints,
we give necessary and sufficient conditions of global optimality expressed in terms of the
Lagrangian function
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
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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