Global optimization using the Newton homotopy-continuation method with application to phase equilibria.

Format:

Book

Thesis/Dissertation

Author/Creator:

Sun, Amy Cha-Tien.

Contributor:

Seider, Warren D., advisor.

University of Pennsylvania.

Language:

English

Subjects (All):

Chemical engineering.

0542.

Penn dissertations--Chemical engineering.

Chemical engineering--Penn dissertations.

Local Subjects:

Penn dissertations--Chemical engineering.

Chemical engineering--Penn dissertations.

0542.

Physical Description:

152 pages

Contained In:

Dissertation Abstracts International 54-12B.

System Details:

Mode of access: World Wide Web.

text file

Summary:

Models of chemical processes often require the solutions of optimization problems. Due to the complexity of these equations and the limitations in numerical techniques, local rather than global optima are likely to be found. In this research, a homotopy-continuation method is applied to locate all of the local (and hence the global) optima associated with nonlinear programs (NLPs) encountered in two classes of chemical process models.

Historically, the homotopy-continuation methods demonstrated globally convergent behavior for the location of a single solution of nonlinear equations. Their ability to locate multiple solutions has only been tested recently. In this research, the Newton homotopy formulation, using a differential arclength algorithm, is investigated for tracking the homotopy path through multiple stationary points of a NLP.

In two problems, one to design a fermentation process and the other to calculate liquid-liquid equilibria, the algorithm locates the global optima by solving the first-order Kuhn-Tucker equations, with the equations of complementary slackness replaced by the Mangasarian equations. Multiple homotopy paths are required to achieve global optimization for the first example, while a single path, passing all of the local optima, was obtained for the second. Despite this success, the homotopy paths for both examples exhibit sharp turning points, which result from the changes in the functional form of the Mangasarian equations. Another characteristic common to both NLPs is the improved convergence when multiple solutions satisfy the homotopy equations at the origin.

The algorithm is also applied to minimize the Gibbs free energy in multiphase equilibria. Before the global minimum is calculated, phase stability analysis is carried out through the minimization of the tangent-plane-distance function (TPDF). The homotopy-continuation algorithm reliably identifies the stationary points of the TPDF. Then, the minima are used to estimate the phase compositions in the search for the global minimum of the Gibbs free energy. A simple initialization scheme, which is applied in all subsequent calculations, is developed to locate the stationary points of the TPDF. HOMPEQ, a new program designed to calculate the global minima of the Gibbs free energy, is tested for nine nonideal mixtures using symmetric and asymmetric models. It is as reliable as the existing techniques, but requires simpler initialization strategies.

Notes:

Thesis (Ph.D. in Chemical Engineering) -- Graduate School of Arts and Sciences, University of Pennsylvania, 1993.

Source: Dissertation Abstracts International, Volume: 54-12, Section: B, page: 6349.

Adviser: Warren D. Seider.

Local Notes:

School code: 0175.

Access Restriction:

Restricted for use by site license.