Proximal methods for nonlinear programming: double regularization and inexact subproblems

This paper describes the first phase of a project attempting to construct an efficient general-purpose nonlinear optimizer using an augmented Lagrangian outer loop with a relative error criterion, and an inner loop employing a state-of-the art conjugate gradient solver. The outer loop can also employ double regularized proximal kernels, a fairly recent theoretical development that leads to fully smooth subproblems. We first enhance the existing theory to show that our approach is globally convergent in both the primal and dual spaces when applied to convex problems. We then present an extensive computational evaluation using the CUTE test set, showing that some aspects of our approach are promising, but some are not. These conclusions in turn lead to additional computational experiments suggesting where to next focus our theoretical and computational efforts.

ABELIANIZED OBSTRUCTION FOR FIXED POINTS OF FIBER-PRESERVING MAPS OF SURFACE BUNDLES

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

Double-strand DNA cleavage induced by oxindole-Schiff base copper(II) complexes with potential antitumor activity

Some oxindole-Schiff base copper(II) complexes have already shown potential antitumor activity towards different cells, inducing apoptosis in a process modulated by the ligand, and having nuclei and mitochondria as main targets. Here, three novel copper(II) complexes with analogous ligands were isolated and characterized by spectroscopic techniques, having their reactivity compared to the so far most active complex in this class. Cytotoxicity experiments carried out toward human neuroblastoma SH-SY5Y cells confirmed its proapoptosis property. DNA cleavage studies were then performed in the presence of these complexes, in order to verify the influence of ligand structural features in its nuclease activity. All of them were able to cause double-strand DNA scissions, giving rise to nicked circular Form II and linear Form III species, in the presence of hydrogen peroxide. Additionally, DNA Form II was also detected in the absence of peroxide when the most active complex, [Cu(isaepy)(2)](2+) 1, was used. In an effort to better elucidate their interactions with DNA, solutions of the different complexes titrated with DNA had their absorption spectra monitored. An absorbance hyperchromism observed at 260 nm pointed to the intercalation of these complexes into the DNA structure. Further, investigations of 2-deoxy-D-ribose (DR) oxidation catalyzed by each of those complexes, using 2-thiobarbituric acid reactive species (TBARS) method, and detection of reactive oxygen species (ROS) formation by spin-trapping EPR, suggested that their mechanism of action in performing efficiently DNA cleavage occurs preferentially, but not only by oxidative pathways. (C) 2007 Elsevier Inc. All rights reserved.

Electrochemical Behaviour of the AA2024 Aluminium Alloy Modified with Self-Assembled Monolayers/Polyaniline Double Films

The electrochemical characteristics of the AA2024 aluminium alloy modified with octadecyltrimethoxysilane (ODTMS) + polyaniline (PANi) and propiltrimethoxysilane (PTMS) + (PANi) were studied in the present work. The results show that the different protective coatings shift the values of corrosion and pit potentials to more positive values making the system nobler and indicate that the double film ODTMS + PANi present the best protection against corrosion characteristics, that is probably due to the two contributions: anodic protection associated with the barrier effect.