Convergence criteria for usable direction methods
Authors
Ellner, Paul M.
ORCID
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Other Contributors
Lemke, Carlton E.
Carter, Richard L.
Ecker, Joseph G.
Rogers, Edwin H.
Carter, Richard L.
Ecker, Joseph G.
Rogers, Edwin H.
Issue Date
1975-06
Keywords
Mathematical programming
Degree
PhD
Terms of Use
This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.
Full Citation
Abstract
The nonlinear programming problem P: maximize f(x) subject to g(x) nonnegative, is considered where f and g are continuously differentiable functions defined on Euclidean n-space, and g is vector-valued. Convergence theorems are obtained that possess the following characteristics: they (1) identify properties of usable direction methods which ensure finite limit points of sequences generated by them are Kuhn-Tucker points of problem P; (2) present convergence criteria that are readily applicable to many usable direction methods; and (3) suggest ways to construct usable direction methods which generate sequences whose finite limit points are Kuhn-Tucker points of problem P. The problem of constructing and analyzing steplength functions which meet the criteria of the convergence theorems is addressed from a unified viewpoint. In addition, several classes of usable direction algorithms are presented whose convergence properties are analyzed via the convergence theorems.
Description
June 1975
School of Science
School of Science
Department
Dept. of Mathematical Sciences
Publisher
Rensselaer Polytechnic Institute, Troy, NY
Relationships
Rensselaer Theses and Dissertations Online Collection
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