A lot of effort in the recent past has been expended on theoretical development, algorithmic investigation, computational testing, and chemical engineering design and science applications of the local optimization algorithms for nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP) problems. There now exist a number of local optimization algorithms and their efficient implementations that are used for small, medium, and large scale problems. There has been much less systematic study on the theoretical developments, algorithmic methodology, computational testing, and application to chemical engineering design and science problems of global optimization approaches. The goal of this research is to develop and apply theoretical, algorithmic and computational techniques for global optimization problems (GOP) that arise in a variety of chemical engineering design and science applications. The PI will investigate several classes of global optimization problems using a primal-relaxed dual global optimization algorithm. In particular, he will focus on: (1) new properties and new formulations of the relaxed dual subproblems; (2) the design of phase and chemical reaction equilibrium systems; (3) the process synthesis of separations, heat recovery networks and reactor systems; (4) bilevel linear and nonlinear optimization problems arising in process design and control; (5) optimum structure(s) determination of clusters of atoms and molecules; and (6) the development of a parallel primal relaxed dual, GOP, approach.
