Many engineering tasks can be formulated as dynamic optimization or op
en-loop optimal control problems, where we search a priori for the inp
ut profiles to a dynamic system that optimize a given performance meas
ure over a certain time period. Further, many systems of interest in t
he chemical processing industries experience significant discontinuiti
es during transients of interest in process design and operation. This
paper discusses three classes of dynamic optimization problems with d
iscontinuities: path-constrained problems, hybrid discrete/continuous
problems, and mixed-integer dynamic optimization problems. In particul
ar, progress toward a general numerical technology for the solution of
large-scale discontinuous dynamic optimization problems is discussed.