Least Relative Change Quasi-Newton Updates for Chemical Engineering Process Optimization

Nguyen, Thai Dong

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Description

Title

Least Relative Change Quasi-Newton Updates for Chemical Engineering Process Optimization

Author(s)

Nguyen, Thai Dong

Issue Date

1993

Doctoral Committee Chair(s)

Stadtherr, Mark A.

Department of Study

Chemical Engineering

Discipline

Chemical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Engineering, Chemical
• Operations Research

Abstract

• Advances in supercomputer architectures and mathematics have enhanced the performance of the equation-based approach in chemical engineering process simulation and design problems. However, the progress in the area of large-scale optimization is achieved at a slower pace thanks to difficulties in approximation of the sparse symmetric Hessian matrix by using traditional sparse least absolute change quasi-Newton updates.
• In this work, four new sparse Hessian updates are derived by minimizing the relative change in the norm of the matrix. The new updates preserve symmetry and sparsity pattern of the Hessian. All four new updates are shown to be invariant to variable scaling, a property possessed only by the good dense least absolute change updates. The secant equation is satisfied in two of the least relative change updates which require the solution for an additional linear system with the same sparsity pattern of the true Hessian. Several important issues in implementing a computer code for large-scale optimization are also discussed. Preliminary numerical experiments demonstrate better performance of the new least relative change updates to previous sparse symmetric updates.

Graduation Semester

1993

Type of Resource

text

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