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Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 2003-2004 MATHEMATICS COLLOQUIUM SERIES 02/23/04 Colloquium DR. YA-XIANG YUAN INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCI./ENGR. COMPUTING Stepsizes for the Steepest Descent Method Abstract:   The steepest descent method is the simplest gradient method for unconstrained optimization. It is well-known that the steepest descent method leads to zig-zags and it converges very slowly (at most linearly) with exact line searches, especially when the optimization problem is ill-conditioned. The Brazilai and Borwein stepsize formulae suggest stepsizes that ensure superlinear convergences of the steepest descent method. In this talk, we will present some recent advances about the choices of different stepsizes for improving the steepest descent method.