phcalamai@water.UUCP (Paul H. Calamai) (03/09/86)
The Department of Systems Design Engineering at the University of Waterloo is proud to announce the following seminar: Speaker: Jorge More, Argonne National Laboratory, Argonne Illinois. Title: Projected Gradients and Conjugate Gradients for Large Scale Problems Date: Tuesday, March 18, 1986. Time: 10:30 a.m. Place: Engineering 2 - Room 1307c (E2-1307c) Abstract:We are interested in the numerical solution of large scale minimization problems subject to linear constraints. Algorithms based on projected gradients are able to drop and add many constraints at each iteration, and this property gives them an important advantage in large scale problems. We introduce and motivate the idea of the projected gradient methods. We review their convergence properties and show that the convergence results are quite strong. In particular, we introduce the notion of a projected gradient and show that the sequence of projected gradients converges to zero. We also show that on nondegenerate problems active and binding sets are identified in a finite number of iterations. We then discuss the current attempts at constructing superlinearly convergent algorithms based on projected gradients, and show that algorithms of the conjugate gradient type are possible and quite attractive.