On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds

We consider a new algorithm, an interior-reflective Newton approach, for the problem of minimizing a smooth nonlinear function of many variables, subject to upper and/or lower bounds on some of the variables. This approach generatesstrictly feasible iterates by using a new affine scaling transformation and following piecewise linear paths (reflection paths). The interior-reflective approach does not require identification of an activity set. In this paper we establish that the interior-reflective Newton approach is globally and quadratically convergent. Moreover, we develop a specific example of interior-reflective Newton methods which can be used for large-scale and sparse problems.Research partially supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under grant DE-FG02-86ER25013.A000, and in part by NSF, AFOSR, and ONR through grant DMS-8920550, and by the Advanced Computing Research Institute, a unit of the Cornell Theory Center which receives major funding from the National Science Foundation and IBM Corporation, with additional support from New York State and members of its Corporate Research Institute.Corresponding author.     

Use of cyclic differential scanning calorimetry

Formation of an activated cellulose (Cellulose) species $$CELLULOSE\xrightarrow[{air}]{{heat}}CELLULOSE*$$ is the designated first stage of cellulose degradation in air [1]. Little is known about either the process or the nature of CELLULOSE^*. The transition, designatedT ₂, is observed as an exotherm around 300°C as the sample temperature is raised. No corresponding endotherm is observed on cooling. The process is therefore not reversible but is repeatable as subsequent reheating results in the exotherm being observed again. The exotherm is also found to be oxygen dependant. The effect of all the flame retardant treatments studied was to reduceT ₂ compared to the value for the untreated cotton.     

Functionalization of single-walled carbon nanotubes via the Bingel reaction

Single-walled carbon nanotubes have been cyclopropanated under Bingel reaction conditions, and the functionalized nanotubes have been characterized by atomic force microscopy using "chemical tagging" techniques.