Filter-Trust-Region Methods for Nonlinear Optimization

This work is concerned with the theoretical study and the implementation of algorithms for solving two particular types of nonlinear optimization problems, namely unconstrained and simple-bound constrained optimization problems. For unconstrained optimization, we develop a new algorithm which uses a filter technique and a trust-region method in order to enforce global convergence and to improve the efficiency of traditional approaches. We also analyze the effect of approximate first and second derivatives on the performance of the filter-trust-region algorithm. We next extend our algorithm to simple-bound constrained optimization problems by combining these ideas with a gradient-projection method. Numerical results follow the proposed methods and indicate that they are competitive with more classical trust-region algorithms.(DOCSC00)--FUNDP, 200

How much do approximate derivatives hurt filter methods?

In this paper, we examine the influence of approximate first and/or second derivatives on the filter-trust-region algorithm designed for solving unconstrained nonlinear optimization problems and proposed by Gould, Sainvitu and Toint in [12]. Numerical experiments carried out on small-scaled unconstrained problems from the CUTE

3D Monitoring of LHCb Inner Tracker

The positions of the Inner Tracker (IT) detectors of the LHCb experiment installed in the LHC at CERN are impacted by the LHCb dipole magnet powering. In the past the movements of the stations have been measured using standard survey methods during magnet tests in shutdown periods. But the survey targets are visible only in very narrow spaces and the access to the IT is very difficult, even impossible in the central region when the detector is closed. Finally the precision of the standard survey measurement is affected by the poor configuration. In 2013 and 2014, during the first long shutdown of the LHC (LS1), the CERN Survey team (EN/MEF-SU) in collaboration with the LHCb Technical Coordination and the EPFL (Ecole Polytechnique Fédérale de LAUSANNE, CH), developed a permanent monitoring system which has been tested and installed in order to allow the 3D position measurement of the IT stations, even during the run periods, with a precision of 100 microns at 1 sigma level. The 3D Monitoring system of the LHCb IT stations is based on opto-electronic BCAM (Brandeis CCD Angle Monitor) sensors, precise low material retro-reflective targets and mechanical elements. This paper summarizes the studies of the proposed system, its configuration and integration in the experiment, as well as the first results obtained