Seminar by Regina Burachik

Seminar by
REGINA BURACHIK
School of Information Technology and Mathematical Sciences
University of South Australia
Australia

 

 

Augmented Lagrangian duality provides zero duality gap and saddle point properties for nonconvex optimization. On the basis of this duality, subgradient-like methods can be applied to the (convex) dual of the original problem. These methods usually recover the optimal value of the problem, but may fail to provide a primal solution. We prove that the recovery of a primal solution by such methods can be characterized in terms of (i) the differentiability properties of the dual function, and (ii) the exact penalty properties of the primal-dual pair. We also connect the property of finite termination with exact penalty properties of the dual pair. In order to establish these facts, we associate the primal-dual pair to a penalty map. This map, which we introduce here, is a convex and globally Lipschitz function, and its epigraph encapsulates information on both primal and dual solution sets.

 

Short Bio:
Regina Burachik is an Associate Professor at University of South Australia, and her current research interests are nonsmooth, convex, and nonconvex optimization. She has also extensive work in the development of algorithms for nonconvex minimization. Her PhD thesis introduced and analyzed solution methods for variational inequalities, the latter being a generalization of the convex constrained optimization problem. She recently co-authored the Springer book "Set-Valued Analysis and Monotone Mappings". Regina is an associate editor of several journals from the area of optimization, including SIAM Journal on Optimization, Applied Mathematics and Computations, Communications in Mathematical Analysis, TOP, and the Australian and New Zealand Journal for Industrial Mathematics. Regina enjoys learning, teaching, supervising and collaborating with others. Her main and only reason for doing math is pleasure.