The Global Convergence of a New Mixed Conjugate Gradient Method for Unconstrained Optimization

We propose and generalize a new nonlinear conjugate gradient method for unconstrained optimization. The global convergence is proved with the Wolfe line search. Numerical experiments are reported which support the theoretical analyses and show the presented methods outperforming CGDESCENT method

Development Status of Adjustable Grazing Incidence Optics for 0.5 Arcsecond X-Ray Imaging

We describe progress in the development of adjustable grazing incidence X-ray optics for 0.5 arcsec resolution cosmic X-ray imaging. To date, no optics technology is available to blend high resolution imaging like the Chandra X-ray Observatory, with square meter collecting area. Our approach to achieve these goals simultaneously is to directly deposit thin film piezoelectric actuators on the back surface of thin, lightweight Wolter-I or Wolter- Schwarschild mirror segments. The actuators are used to correct mirror figure errors due to fabrication, mounting and alignment, using calibration and a one-time figure adjustment on the ground. If necessary, it will also be possible to correct for residual gravity release and thermal effects on-orbit. In this paper we discuss our most recent results measuring influence functions of the piezoelectric actuators using a Shack-Hartmann wavefront sensor. We describe accelerated and real-time lifetime testing of the piezoelectric material, and we also discuss changes to, and recent results of, our simulations of mirror correction

On implicit-factorization constraint preconditioners

Recently Dollar and Wathen [14] proposed a class of incomplete factorizations for saddle-point problems, based upon earlier work by Schilders [40]. In this paper, we generalize this class of preconditioners, and examine the spectral implications of our approach. Numerical tests indicate the efficacy of our preconditioners