Tuesday, April 9 at 4:00pm to 5:00pm
Mohler Laboratory, 453
200 W Packer Ave., Bethlehem, PA 18015
Title: Novel polyhedral relaxations for mixed-integer polynomial optimization problems
We consider the multilinear set defined by a collection of multilinear terms over the unit hypercube. Such sets appear in factorable reformulations of many types of mixed-integer nonlinear optimization problems. Utilizing an equivalent hypergraph representation for the multilinear set, we derive various types of facet defining inequalities for its polyhedral convex hull and present a number of tightness results based on the acyclicity-degree of the underlying hypergraph. Subsequently, we detail on the complexity of corresponding separation problems and embed the proposed cut generation algorithm at every node of the branch-and-reduce global solver BARON. Extensive computational results will be presented.
Aida Khajavirad is a visiting Assistant Professor at the department of Management Science and Information systems at Rutgers school of Business. She is also a visiting academic at the Courant Institute of Mathematical Sciences of New York University. In the past Aida has held positions as a Research Associate in the Center for Advanced Process Decision-making of Carnegie Mellon University, Assistant Professor of Operations Research at the University of Texas at Austin and Research Scientist in the theory group of IBM T.J. Watson research center. Aida’s research interest lies at the interface of convex analysis and nonconvex optimization. Her current work is focused on both theoretical and algorithmic aspects of global optimization of nonconvex mixed-integer nonlinear optimization problems with applications in operations research, computer science, engineering and economics. Her work has been funded by NSF and DOE and has been recognized by the INFORMS Optimization Society Prize for young researchers.