My research

• Using optimization techniques for diagnosing hidden vulnerabilities in power (electricity) networks.  Several national-scale blackouts took place in the recent past, with significant consequences.  More such blackouts can be expected.  Even though large-scale blackouts are quite rare, when they do happen the impact can be dire.  Blackouts are rare because modern power grids are robust; yet vulnerabilities do exist.  The search for hidden vulnerabilities, roughly speaking, embodies finding an instance where a limited amount of damage can cause a grid to collapse.  It is important to frame the search for such vulnerabilities in a completely agnostic manner.  We are using techniques reminiscent of robust optimization in order to develop computational tools that effectively incorporate the physics of power networks and scale well to large cases. Further material available here.

• Fundamental methodologies for integer programming.  We are studying techniques for provably tightening formulations of mixed-integer programs.  Here, 'provably' means that we seek guarantees (e.g. error bounds).  Thus, in an ideal setting an improved formulation is polynomially large and guarantees a 'small' approximation error.  Our primary technique in this context is the use of carefully selected combinatorial disjunctions.
  

• Robust optimization.  Broadly speaking, robust optimization concerns optimization problems where a fictitious adversary obscures the problem definition.  We are interested in computationally practicable versions of Benders' algorithm, and their interpretation as a game between an optimizer and the adversary.