A variante de Barzilai-Borwein do método gradiente
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2016-04-29
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Universidade Federal de Goiás
Resumo
The gradient method is a classical optimization methods to minimize a function. This
method deserves special mention for its simplicity and easy understanding. This work is
based on the study of the gradient method with step size given by the variant Barzilai-
Borwein. Our goal is to present the convergence of the method with this variant. First we
will study the two-dimensional case, for strictly convex quadratic functions. In this case,
besides obtaining the convergence of the method, we see that such convergence occurs
with R-superlinear rate. In the final part of the work, we will study the method with the
variant Barzilai-Borwein not necessarily quadratic functions, concluding that the method
converges.
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MOURA, Abssan Matuzinhos de. A variante de Barzilai-Borwein do método gradiente. 2016. 59 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2016.