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Cluster :  Nonlinear Programming

Session Information  : Friday Jul 17, 14:45 - 16:15

Title:  Large-Scale Nonlinear Optimization
Chair: Roummel Marcia,Associate Professor, University of California, Merced, 5200 N. Lake Road, Merced Ca 95343, United States of America, rmarcia@ucmerced.edu

Abstract Details

Title: A High-accuracy Sr1 Trust-region Subproblem Solver for Large-scale Optimization
 Presenting Author: Jennifer Erway,Associate Professor, Wake Forest University, Winston-Salem NC, United States of America, erwayjb@wfu.edu
 Co-Author: Johannes Brust,University of California, Merced, 5200 N. Lake Road, Merced CA, United States of America, jbrust@ucmerced.edu
 Roummel Marcia,Associate Professor, University of California, Merced, 5200 N. Lake Road, Merced Ca 95343, United States of America, rmarcia@ucmerced.edu
 
Abstract: In this talk we present an SR1 trust-region subproblem solver for large-scale unconstrained optimization. This work makes use the exact leftmost eigenvalue, obtainable from the compact representation of an SR1 matrix, to address the so-called "hard case". In all cases, we are able to obtain high-accuracy solutions. Numerical results will be presented.
  
Title: Preconditioning for Optimization Problem with Nonlocal Operators
 Presenting Author: Ekkehard Sachs,University of Trier, Trier, Germany, sachs@uni-trier.de
 
Abstract: Nonlocal operators occur in peridynamics, cell adhesion processes and the modeling of option prices of jump diffusion type. Optimization comes into play when parameters have to be estimated by fitting the output data. It is obvious that for a fast numerical solution preconditioning is essential. Often the point of view is taken that the diffusive, i.e. local, part of the operator needs preconditioning whereas the integral, i.e. nonlocal part is of smoothing type, even a compact operator, and hence no preconditioning is necessary. However, we show in this talk that this is misleading because the smoothing property depends strongly on the shape of the distribution function or kernel. We underscore this observation by numerical experiments.
  
Title: Recent Developments in SQP Methods for Large-Scale Nonlinear Optimization
 Presenting Author: Elizabeth Wong,University of California, San Diego, Department of Mathematics, 9500 Gilman Drive, # 0112, La Jolla CA 92093-0112, United States of America, elwong@ucsd.edu
 Co-Author: Philip E. Gill,UC San Diego, Department of Mathematics, La Jolla CA 92039-0112, United States of America, pgill@ucsd.edu
 Michael Saunders,Department of Management Science and Engineering, Stanford University, Stanford CA 94305-4121, United States of America, saunders@stanford.edu
 
Abstract: We discuss some practical issues associated with the formulation of sequential quadratic programming (SQP) methods for large-scale nonlinear optimization. Numerical results are presented for the software package SNOPT, which uses a positive-definite quasi-Newton approximate Hessian or an exact Hessian.