Title

An Acceleration Method for Dogleg Methods in Simple Singular Regions

Document Type

Article

Date of Original Version

1-1-1998

Abstract

The behavior of dogleg methods in singular regions that have a one-dimensional null space is studied. A two-tier approach of identifying singular regions and accelerating convergence to a singular point is proposed. It is shown that singular regions are easily identified using a ratio of the two-norm of the Newton step to the two-norm of the Cauchy step since Newton steps tend to infinity and Cauchy steps tend to zero as a singular point is approached. Convergence acceleration is accomplished by bracketing the singular point using a projection of the gradient of the two-norm of the process model functions onto the normalized Newton direction in conjunction with bisection, thus preserving the global convergence properties of the dogleg method. Numerical examples for a continuous-stirred tank reactor and vapor-liquid equilibrium flash are used to illustrate the reliability and effectiveness of the proposed approach. Several geometric illustrations are presented.

Publication Title

Industrial and Engineering Chemistry Research

Volume

37

Issue

4

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