Abstract:
We develop a branch-and-bound algorithm for the D-optimality problem (D-opt), a central problem in statistical design theory, based on two bounds derived from convex relaxations, the ``natural bound'' and the ``Γ-bound''. We describe a procedure to fix variables based on convex duality. We demonstrate that the Γ-bound for the binary version of D-opt with a particular variable fixing is precisely the ``complementary Γ-bound'' for the so-called ``Data-Fusion problem''. Further, we present theoretical results showing some relations between different bounds. We propose local-search heuristics for D-opt and analyze different strategies to compute search directions and step sizes for each iteration of them. Finally, we present numerical experiments concerning a B&B algorithm based on our results. This is a joint work with Jon Lee and Gabriel Ponte.

Bio:
Marcia Fampa is a Professor at the Federal University of Rio de Janeiro (UFRJ), where she has been since 1997. She is at the Alberto Luiz Coimbra Institute for Graduate Studies and Research in Engineering (COPPE), at UFRJ, where she has supervised more than 32 PhD and master's students. She was a board member of the Brazilian Society of Operations Research (SOBRAPO). Marcia did her undergraduate studies at the Pontifical Catholic University of Rio de Janeiro (PUC/RJ), receiving an engineering degree in 1987. She received her PhD Degree in Systems and Computer Engineering from the Federal University of Rio de Janeiro in 1996. In 1995 and in 2005 she was a visiting researcher at the University of Iowa. She is currently a research visitor at the University of Michigan. Her main research interest is Mixed Integer Nonlinear Programming (MINLP), with a focus on the development of convex relaxations for MINLP problems.