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 |uhttp://pqdd.sinica.edu.tw/twdaoapp/servlet/
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