Preconditioning issues in the numerical solution of nonlinear equations and nonlinear least squares

Second order methods for optimization call for the solution of sequences of linear systems. In this survey we will discuss several issues related to the preconditioning of such sequences. Covered topics include both techniques for building updates of factorized preconditioners and quasi-Newton approaches. Sequences of unsymmetric linear systems arising in Newton-Krylov methods will be considered as well as symmetric positive definite sequences arising in the solution of nonlinear least-squares by Truncated Gauss-Newton methods

Global convergence of a new hybrid Gauss-Newton structured BFGS method for nonlinear least squares problems

2009-2010 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Experimental Investigation of Quasi-Newton Approaches to a Learning Problem in Electronic Negotiation

The recent growth in electronic commerce has motivated the development of semi-autonomous negotiation systems capable of implementing multiple negotiations simultaneously. Different approaches have recently been presented in the literature with the aim of providing a solution to this growing market segment. The current thesis presents an examination of optimization approaches for learning the parameters of a time-dependent decision-function that has recently obtained significant interest in the negotiation literature. Twelve different nonlinear optimization variants are evaluated using 800 problems, and the resulting 9600 runs are statistically analyzed on four different performance measures. Potential implications of our analysis are discussed for their possible use in the context of electronic negotiatio