Homotopy continuation methods for computer-aided process design

• Published in: Computers & chemical engineering Vol. 11; no. 1; pp. 7 - 25
• Main Authors: Wayburn, T.L., Seader, J.D.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 1987; Elsevier
• Subjects: Applications of mathematics to chemical engineering. Modeling. Simulation. Optimization; Applied sciences; Chemical engineering; Exact sciences and technology; Equation system solving; Linear equation; Flowsheeting; Chemical engineering; Homotopy; Computer aided design
• ISSN: 0098-1354; 1873-4375
• DOI: 10.1016/0098-1354(87)80002-9

Homotopy continuation methods have been used by the authors and others to solve difficult chemical engineering flowsheeting and design problems involving the solution of simultaneous nonlinear equations. Such methods can fail when: (1) the homotopy path, which one follows from the solution of a simple problem to the solution of the original (difficult) problem, returns to a second solution of the simple problem; (2) the homotopy path strikes an interior boundary of the domain of definition of the original (vector-valued) function; and (3) the homotopy path goes off to infinity. For the first two modes of failure, the use of an affine homotopy is discussed here as a possible remedy. Failure due to an unbounded homotopy path is the subject of current research.