Monday, November 20

3108 Etcheverry Hall, 3:30 p.m. - 5:00 p.m.

Abstract:  Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in ever more larger scale. However, the traditional approaches for solving RO formulations based on building and solving robust counterparts or the iterative approaches utilizing nominal feasibility oracles can be prohibitively expensive and thus significantly hinder the scalability of RO paradigm. 

We present a general and flexible iterative framework to solve robust convex optimization problems that is built on a fully online first-order paradigm. In contrast to the existing literature, a key distinguishing feature of our approach is that it requires access to only cheap first-order oracles for the original problem that are remarkably cheaper than pessimization or nominal feasibility oracles, while maintaining the same convergence rates. This, in particular, makes our approach much more scalable and hence preferable in large-scale applications. In the case of strongly convex functions, we also establish a new improved iteration complexity addressing an open question in the literature. Motivated by a robust portfolio optimization problem, we demonstrate our approach on robust quadratic programs with ellipsoidal uncertainty.

If time permits, we will discuss connections and applicability of our online framework in the context of joint estimation and optimization problems.

This is joint work with Nam Ho-Nguyen (Carnegie Mellon University, USA).

Fatma is an Associate Professor of Operations Research at Tepper School of BusinessCarnegie Mellon University. She is also affiliated with the Algorithms Combinatorics and Optimization (ACO) PhD Program

 

Monday, November 27

3108 Etcheverry Hall, 3:30 p.m. - 5:00 p.m.

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). 

 

Monday, April 2

3108 Etcheverry Hall, 3:30 p.m. - 5:00 p.m.

We develop a framework to analyze the consequences of alternative designs for interbank networks, in which a failure of one bank may lead to others. Earlier work had suggested that, provided shocks were not too large (or too correlated), denser networks were preferred to more sparsely connected networks because they were better able to absorb shocks. With large shocks, especially when systems are non-conservative, the likelihood of costly bankruptcy cascades increases with dense networks. Governments, worried about the cost of bailouts, have proposed bail-ins, where creditors of defaulting banks voluntarily contribute to rescue their debtors.
However, credibility and enforceability were again at issue.  How can the government enforce private sector involvement when the private sector knows that in the absence of its cooperation, the government would nonetheless proceed with a bailout? While a few bail-ins have been observed in practice, it has not been understood until recently under which conditions they exist. 

We answer in the affirmative the key question of whether credible bail-in strategies exist, showing that this strongly depends on the network structure. We model the coordination of a rescue consortium between a social planner and the banks as a sequential game. We show that the equilibrium welfare losses are generically unique, and characterize the subgame perfect equilibrium of the game yielding the optimal intervention plan.

Our findings reverse the presumptions in earlier works and promote sparsely connected networks over densely connected ones because (i) the no-intervention threat exhibits a phase transition and becomes more credible for large shocks and (ii) banks' contributions to the coordinated bail-in plan are larger.  

This is joint work with Benjamin Bernard and Joseph Stiglitz.