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.  

Otto Klitgord and Major Benjamin Namm

Otto Klitgord is depicted giving Benjamin H. Namm, chairman of the college's Board of Trustees a degree. Otto Klitgord was the first president of the New York City College of Technology. He was named director of the New York State Institute of Applied Arts and Sciences when it was formed in the 1946 and became president in the 1950s when the administration was reorganized. Klitgord served until 1960, making his tenure as president the longest in City Tech's history.

Innocents Abroad: Gary Newton manages global efforts to help the world's most vulnerable children

Gary Newton ’72 manages global efforts to help vulnerable kids.