Process optimization in equation-oriented (EO) modeling environments favors the gradient-based optimization algorithms by their abilities to provide accurate Jacobian matrices

via

automatic or symbolic differentiation. However

computational inefficiencies including that in initial-point-finding for Newton type methods have significantly limited its application. Recently

progress has been made in using a pseudo-transient (PT) modeling method to address these difficulties

providing a fresh way forward in EO-based optimization. Nevertheless

research in this area remains open

and challenges need to be addressed. Therefore

understanding the state-of-the-art research on the PT method

its principle

and the strategies in composing effective methodologies using the PT modeling method is necessary for further developing EO-based methods for process optimization. For this purpose

the basic concepts for the PT modeling and the optimization framework based on the PT model are reviewed in this paper. Several typical applications

e.g

.

complex distillation processes

cryogenic processes

and optimizations under uncertainty

are presented as well. Finally

we identify several main challenges and give prospects for the development of the PT based optimizati

on methods.