Abstract: Practical exact methods for global optimization of mixed-integer nonlinear optimization formulations rely on convex relaxation. Then, one way or another (via refinement and/or disjunction), global optimality is sought. Success of this paradigm depends on balancing tightness and lightness of relaxations. We will investigate this from a mathematical viewpoint, comparing polyhedral relaxations via their volumes. Specifically , I will present some results concerning: fixed charge problems, vertex packing in graphs, boolean quadratic formulations, and convexification of monomials in the context of spatial branch-and-bound" for factorable formulations. Our results can be employed by users (at the modeling level) and by algorithm designers/implementers alike.
Short bio: Jon Lee is the G. Lawton and Louise G. Johnson Professor of Engineering at the University of Michigan. He received his Ph.D. from Cornell University. Jon has previously been a faculty member at Yale University and the University of Kentucky, and an adjunct professor at New York University. He was a Research Staff member at the IBM T.J. Watson Research Center, where he managed the mathematical programming group. Jon is author of ~120 papers, the text "A First Course in Combinatorial Optimization" (Cambridge University Press), and the open-source book "A First Course in Linear Optimization" (Reex Press). He was the founding Managing Editor of the journal Discrete Optimization (2004-06), he is currently co-Editor of the journal Mathematical Programming, and he is on the editorial boards of the journals Optimization and Engineering, and Discrete Applied Mathematics. Jon was Chair of the Executive Committee of the Mathematical Optimization Society (2008-10), and Chair of the INFORMS Optimization Society (2010-12). He was awarded the INFORMS Computing Society Prize (2010), and he is a Fellow of INFORMS (since 2013).