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Liu Bie Ju Centre for Mathematical Sciences
City University of Hong Kong
Mathematical Analysis and its Applications
Colloquium

Organized by Prof. Philippe G. Ciarlet and Prof. Roderick Wong

Beyond Symmetric Broyden for Updating Quadratic
Models in Minimization without Derivatives

by
Professor M.J.D. Powell
University of Cambridge, U.K.
and
City University of Hong Kong

Date: Feb 10, 2010 (Wednesday)
Time:4:30 pm to 5:30 pm
Venue: Room B6605 (College Conference Room)
Blue Zone, Level 6, Academic Building
City University of Hong Kong

ABSTRACT: Some highly successful algorithms for unconstrained minimization without derivatives construct changes to the variables by applying trust region methods to quadratic approximations to the objective function, F say. A quadratic model has (n+1)(n+2)/2 independent parameters, where n is the number of variables, but typically each new model has to interpolate only 2n+1 values of F. The symmetric Broyden method takes up the remaining freedom by minimizing the Frobenius norm of the difference between the second derivative matrices of the old and new models, which usually works well in practice. We consider an extension of this technique that combines changes in first derivatives with changes in second derivatives. A way of implementing it approximately in only of magnitude n squared operations per iteration is described briefly. Numerical results are given too, but they are not encouraging, except in a case where very high accuracy is required in the final vector of variables.

** All interested are welcome **

For enquiry: 3442-9816