Newton`s iterates can converge to non-stationary points

In this note we discuss the convergence of Newton`s method for minimization. We present examples in which the Newton iterates satisfy the Wolfe conditions and the Hessian is positive definite at each step and yet the iterates converge to a non-stationary point. These examples answer a question posed by Fletcher in his 1987 book Practical methods of optimization.

Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.

Le Statut comparé de l'autofiction chez Benjamin Constant et Amélie Nothomb : une histoire de genre?

Le genre autobiographique, malgré une popularité qui ne se dément pas depuis deux siècles, ne bénéficie pas d’une définition claire. Cet article se propose de montrer que cela est sans doute dû à l’hybridité intrinsèque de ce genre qui se traduit aussi par un pacte autobiographique complexe. Plus précisément, en s’appuyant sur les cas de Constant et de Nothomb, sera démontré que la lecture qui est faite des écrits intimes détermine bien souvent le genre. En ce qui concerne en particulier ces deux auteurs, leur personnalité changeante, contradictoire voire affabulatoire repousse le genre autobiographique dans ses limites, illustrent l’adage selon lequel le roman est plus vrai que la réalité vécue.  

Exploring the benefits and pitfalls of using mutual wills

The purpose of this article is to consider a peculiar type of will known in equity as a mutual will. The major focus is a consideration of the interplay of the legal effect of mutual wills and the practical use of such wills, It is hoped that this discussion will assist legal practitioners in identifying those clients who may benefit from executing mutual wills, identifying those clients who might intend to execute mutual wills, advising clients as to the pros and cons of mutual wills and the benefits of accompanying such wills with a deed or contract.

Language, experience and professional learning (what Walter Benjamin can teach us)

This essay raises questions about how language educators might construct and further develop their epistemology of practice in and through the situations in which they work from day to day. The occasion for this paper is our work as guest editors of a special issue of L-1: Educational Studies in Language and Literature, when we invited L1 teachers to reflect on the role that language plays in their professional learning, whether it be in the form of conversations with peers, reflective writing, or by other means. We begin this essay by locating our reflections within our current policy context, namely the standards-based reforms that have come to dominate educational thinking around the world, offering a brief critique of the values and attitudes embedded within them. We then outline a philosophical framework as an alternative to the world-view reflected by such reforms, focusing specifically on the work of Walter Benjamin. In the final sections, we review our work as guest editors of the special issue of L-1, reflecting on what we have learned from the papers we have assembled for this issue, and locating our learning within the philosophical framework that we have drawn from Benjamin. We argue that it is timely for language educators to articulate the assumptions that inhere within their work, in contradistinction to the common sense embedded in standards. Thus we might begin to reconceptualise the relation between language, experience and professional learning in opposition to the hegemony of standards.