Title page for ETD etd-265913459731541


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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