Title:
New perspectives on sufficient conditions for local optimality
Abstract:
In nonconvex optimization, not only the objective but even the feasible set may lack convexity. It may seem therefore that the concepts and methodology of convex optimization can have no longer have a fundamental role, but this is actually wrong. Standard sufficient conditions for local optimality in nonlinear programming and its extensions actually turn out to correspond to characterizing optimality in terms of a local convex-concave-type saddle point of an augmented Lagrangian function. This offers new perspectives in how to think about sufficient conditions and their role in supporting computational methods.
Biography:
Terry Rockafellar was educated at Harvard University, where he received his doctorate in mathematics in 1963. Not long afterward, he joined the mathematics faculty at the University of Washington in Seattle and is now professor emeritus there.
His research interests have centered on problems of optimization and developing the mathematics associated with them, in particular convex analysis and variational analysis. He has also worked on numerical methodology and the special challenges of optimization in dynamical systems and stochastic systems, expanding into the theory of risk and its applications in finance. His current efforts are focused especially on augmented Lagrangians and schemes of problem decomposition.
Rockafellar is the author of over 250 publications, including a couple of books that have become very highly cited. He has received many prizes for his work and has been awarded the degree of doctor honoris causa by universities in the Netherlands, France, Spain, and Chile.