Thesis (D.A.)--Illinois State University, 1990. / Title from title page screen, viewed November 16, 2005. Dissertation Committee: Stephen Friedberg (chair), John Dossey, George Kidder, Michael Plantholt, Robert Ritt. Includes bibliographical references (leaves 22-23) and abstract. Also available in print.

published_or_final_version / abstract / Mathematics / Master / Master of Philosophy

We study the development of nonlinear conjugate gradient methods, Fletcher Reeves (FR) and Polak Ribiere (PR). FR extends the linear conjugate gradient method to nonlinear functions by incorporating two changes, for the step length αk a line search is performed and replacing the residual, rk (rk=b-Axk) by the gradient of the nonlinear objective function. The PR method is equivalent to FR method for exact line searches and when the underlying quadratic function is strongly convex. The PR method is basically a variant of FR and primarily differs from it in the choice of the parameter βk. On applying the nonlinear Rosenbrock function to the MATLAB code for the FR and the PR algorithms we observe that the performance of PR method (k=29) is far better than the FR method (k=42). But, we observe that when the MATLAB codes are applied to general nonlinear functions, specifically functions whose minimum is a large negative number not close to zero and the iterates too are large values far off from zero the PR algorithm does not perform well. This problem with the PR method persists even if we run the PR algorithm for more iterations or with an initial guess closer to the actual minimum. To improve the PR algorithm we suggest finding a better weighing parameter βk, using better line search method and/or using specific line search for certain functions and identifying specific restart criteria based on the function to be optimized.

Thesis (Ph. D.)--Oregon State University, 1983. / Typescript (photocopy). Includes bibliographical references (leaves 71-74). Also available on the World Wide Web.

Thesis(Ph.D.)--Case Western Reserve University, 2010 / Title from PDF (viewed on 2009-12-30) Department of Electrical Engineering and Computer Science Includes abstract Includes bibliographical references and appendices Available online via the OhioLINK ETD Center

Thesis (M.S.)--University of Florida, 2002. / Title from title page of source document. Document formatted into pages; contains ix, 71 p. Includes vita. Includes bibliographical references.

published_or_final_version / Mathematics / Master / Master of Philosophy

No description available.

Thesis (Ph. D.)--University of Washington, 1993. / Vita. Includes bibliographical references (leaves [129]-133).

Thesis (M. Phil.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.