Infrastructure networks like gas and power grids deliver
critical services and need to be operated with a high degree of
reliability. However, these networks are subject to growing amounts of
uncertainty due to intermittent renewable generation sources,
uncertainty in flexible demand resources and interdependence between
networks. Further, analyzing the behavior of these networks is
complicated because of the nonlinear nature of the equations
describing the steady-state behavior. In recent years, we have
developed novel techniques for "inner feasible" approximations of
nonconvex sets that describe allowable operating points for
infrastructure systems. We analyze the tightness of these
characterizations, and describe applications of these techniques for
robust optimization in infrastructure networks. This is the first
general approach for robust nonconvex optimization problems with
feasibility guarantees.

This is joint work with Konstantin Turitysn, Hung Nguyen, Suhyoun Yu,
Enrique Mallada and John Simpson-Porco.