Numerical experience with a reduced Hessian method for large scale constrained optimization

Lorenz T. Biegler; Jorge Nocedal; Claudia Schmid; David Ternet

doi:10.1023/A:1008723031056

Numerical experience with a reduced Hessian method for large scale constrained optimization

Lorenz T. Biegler, Jorge Nocedal, Claudia Schmid, David Ternet

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

Abstract

The reduced Hessian SQP algorithm presented in Biegler et al. is developed in this paper into a practical method for large-scale optimization. The novelty of the algorithm lies in the incorporation of a correction vector that approximates the cross term Z^T WY p_Y. This improves the stability and robustness of the algorithm without increasing its computational cost. The paper studies how to implement the algorithm efficiently, and presents a set of tests illustrating its numerical performance. An analytic example, showing the benefits of the correction term, is also presented.

Original language	English (US)
Pages (from-to)	45-67
Number of pages	23
Journal	Computational Optimization and Applications
Volume	15
Issue number	1
DOIs	https://doi.org/10.1023/A:1008723031056
State	Published - Jan 2000

ASJC Scopus subject areas

Control and Optimization
Computational Mathematics
Applied Mathematics

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abstract = "The reduced Hessian SQP algorithm presented in Biegler et al. is developed in this paper into a practical method for large-scale optimization. The novelty of the algorithm lies in the incorporation of a correction vector that approximates the cross term ZT WY pY. This improves the stability and robustness of the algorithm without increasing its computational cost. The paper studies how to implement the algorithm efficiently, and presents a set of tests illustrating its numerical performance. An analytic example, showing the benefits of the correction term, is also presented.",

author = "Biegler, {Lorenz T.} and Jorge Nocedal and Claudia Schmid and David Ternet",

note = "Funding Information: ⁄These authors were supported by the Engineering Design Research Center, an NSF Center at Carnegie Mellon as well as through a grant from Bayer Corporation. †This author was supported by National Science Foundation Grant CCR-9625613, and by Department of Energy Grant DE-FG02-87ER25047.",

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AU - Nocedal, Jorge

AU - Schmid, Claudia

AU - Ternet, David

N1 - Funding Information: ⁄These authors were supported by the Engineering Design Research Center, an NSF Center at Carnegie Mellon as well as through a grant from Bayer Corporation. †This author was supported by National Science Foundation Grant CCR-9625613, and by Department of Energy Grant DE-FG02-87ER25047.

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AB - The reduced Hessian SQP algorithm presented in Biegler et al. is developed in this paper into a practical method for large-scale optimization. The novelty of the algorithm lies in the incorporation of a correction vector that approximates the cross term ZT WY pY. This improves the stability and robustness of the algorithm without increasing its computational cost. The paper studies how to implement the algorithm efficiently, and presents a set of tests illustrating its numerical performance. An analytic example, showing the benefits of the correction term, is also presented.

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Numerical experience with a reduced Hessian method for large scale constrained optimization

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