Lectures on

Lagrange-type Functions in Constrained Non-Convex Optimization

by

Professor Yang Xiaoqi

Department of Applied Mathematics

The Hong Kong Polytechnic University

Hong Kong

3:00pm – 4:00pm, 24 and 25 March 2005

Background

Lagrange and penalty function methods provide a powerful approach, both as a theoretical tool and a computational vehicle, for the study of constrained optimization problems. However, for a nonconvex constrained optimization problem, the classical Lagrange primal-dual method may fail to find a minimum as a zero duality gap is not always guaranteed. A large penalty parameter is, in general, required for classical quadratic penalty functions in order that minima of penalty problems are a good approximation to those of the original constrained optimization problems. It is well-known that penalty functions with too large parameters cause an obstacle for numerical implementation. Thus the question arises how to generalize classical Lagrange and penalty functions, in order to obtain an appropriate scheme for reducing constrained optimization problems to unconstrained ones that will be suitable for sufficiently broad classes of optimization problems from both the theoretical and computational viewpoints.

In these lectures, we will investigate the following topics:

1) Duality and exact penalization via a generalized augmented Lagrangian.

2) Partially strictly monotone and nonlinear penalty functions for constrained mathematical programs.

About the Speaker

Dr Yang Xiaoqi is an Associate Professor in Department of Applied Mathematics, The Hong Kong Polytechnic University. He got his BSc degree in Chongqing Jianzhu University (now Chongqing University) in 1982 and his PhD degree from The University of New South Wales in 1994. He was a Postdoctoral Fellow and then Lecturer in The University of Western Australia from 1994 to 1999. Dr Yang was awarded an ISI Citation Classic in 2000. Dr Yang has published 3 research monographs, 3 edited books and over 120 research papers in international prestigious journals. Dr Yang is now an associate editor for a number of international journals, including Journal of Optimization Theory and Applications, and a Board member of The Pacific Optimization Research Activity Group (POP).

* * * ALL ARE WELCOME * * *