Type of Document Dissertation Author Kim, Jinhyo URN etd-265913459731541 Title Iterated Grid Search Algorithm on Unimodal Criteria Degree PhD Department Statistics Advisory Committee
Advisor Name Title Krutchkoff, Richard G. Committee Co-Chair Terrell, George R. Committee Co-Chair Arnold, Jesse C. Committee Member Coakley, Clint W. Committee Member Foutz, Robert Committee Member Keywords
- none
Date of Defense 1997-06-02 Availability unrestricted Abstract The unimodality of a function seems a simple
concept. But in the Euclidean space R^m,
m=3,4,..., it is not easy to define. We have an
easy tool to find the minimum point of a unimodal
function. The goal of this project is to formalize
and support distinctive strategies that typically
guarantee convergence. Support is given both by
analytic arguments and simulation study.
Application is envisioned in low-dimensional but
non-trivial problems. The convergence of the
proposed iterated grid search algorithm is
presented along with the results of particular
application studies. It has been recognized that the
derivative methods, such as the Newton-type
method, are not entirely satisfactory, so a variety
of other tools are being considered as alternatives.
Many other tools have been rejected because of
apparent manipulative difficulties. But in our
current research, we focus on the simple algorithm
and the guaranteed convergence for unimodal
function to avoid the possible chaotic behavior of
the function. Furthermore, in case the loss function
to be optimized is not unimodal, we suggest a
weaker condition: almost (noisy) unimodality,
under which the iterated grid search finds an
estimated optimum point. Subject Classification:
statistical computing, nonlinear estimation,
statistical optimization, statistical simulation Key
Words: Iterated Grid Search, grid, dichotomous
search, unimodality, quasi-convexity, envelope,
condition number, derivative-free
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