The accurate analysis of cross-talk noise in VLSI chIPs must consider the timing when signals can interfere, i.e., the switching windows. It is important to determine the time-alignment of signal switching events that cause maximal cross-talk noise. Moreover, it is necessary to include the effects of process and environmental variations, as they strongly affect the switching windows, and further complicate the computation of the worst possible noise. We present a general formulation of the worst case noise analysis problem as a mixed-integer-linear-program, (MILP). The formulation captures elaborate cross-talk models that include variational switching windows, victim sensitivity windows, discontinuous switching windows, diversely shaped noise pulses, and logic constraints on switching activity. We demonstrate that our technique correctly predicts the worst noise pulse, including cases even where conventional approaches fail.