MARC 主機 00000nam  2200325   4500 
001    AAI3473216 
005    20121102113831.5 
008    121102s2011    ||||||||||||||||| ||eng d 
020    9781124873749 
035    (UMI)AAI3473216 
040    UMI|cUMI 
100 1  Mohr, Darin Griffin 
245 10 Hybrid Runge-Kutta and quasi-Newton methods for 
       unconstrained nonlinear optimization 
300    168 p 
500    Source: Dissertation Abstracts International, Volume: 72-
       12, Section: B, page: 7455 
500    Adviser: Laurent O. Jay 
502    Thesis (Ph.D.)--The University of Iowa, 2011 
520    Finding a local minimizer in unconstrained nonlinear 
       optimization and a fixed point of a gradient system of 
       ordinary differential equations (ODEs) are two closely 
       related problems. Quasi-Newton algorithms are widely used 
       in unconstrained nonlinear optimization while Runge-Kutta 
       methods are widely used for the numerical integration of 
       ODEs. In this thesis, hybrid algorithms combining low-
       order implicit Runge-Kutta methods for gradient systems 
       and quasi-Newton type updates of the Jacobian matrix such 
       as the BFGS update are considered. These hybrid algorithms
       numerically approximate the gradient flow, but the exact 
       Jacobian matrix is not used to solve the nonlinear system 
       at each step. Instead, a quasi-Newton matrix is used to 
       approximate the Jacobian matrix and matrix-vector 
       multiplications are performed in a limited memory setting 
       to reduce storage, computations, and the need to calculate
       Jacobian information 
520    For hybrid algorithms based on Runge-Kutta methods of 
       order at least two, a curve search is implemented instead 
       of the standard line search used in quasi-Newton 
       algorithms. Stepsize control techniques are also performed
       to control the stepsize associated with the underlying 
       Runge-Kutta method 
520    These hybrid algorithms are tested on a variety of test 
       problems and their performance is compared with that of 
       the limited memory BFGS algorithm 
590    School code: 0096 
650  4 Applied Mathematics 
690    0364 
710 2  The University of Iowa.|bApplied Mathematical & 
       Computational Sciences 
773 0  |tDissertation Abstracts International|g72-12B 
856 40 |u