A method to guarantee local convergence for sequential quadratic programming with poor Hessian approximation

Tuan T. Nguyen, Mircea Lazar, Hans Butler

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

1 Citation (Scopus)

Abstract

Sequential Quadratic Programming (SQP) is a powerful class of algorithms for solving nonlinear optimization problems. Local convergence of SQP algorithms is guaranteed when the Hessian approximation used in each Quadratic Programming subproblem is close to the true Hessian. However, a good Hessian approximation can be expensive to compute. Low cost Hessian approximations only guarantee local convergence under some assumptions, which are not always satisfied in practice. To address this problem, this paper proposes a simple method to guarantee local convergence for SQP with poor Hessian approximation. The effectiveness of the proposed algorithm is demonstrated in a numerical example.

LanguageEnglish
Title of host publication2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages3781-3786
Number of pages6
ISBN (Electronic)978-1-5090-2873-3
ISBN (Print)978-1-5090-2874-0
DOIs
StatePublished - 18 Jan 2018
Event56th IEEE Conference on Decision and Control (CDC 2017) - Melbourne, Australia
Duration: 12 Dec 201715 Dec 2017
Conference number: 56
http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=8253407

Conference

Conference56th IEEE Conference on Decision and Control (CDC 2017)
Abbreviated titleCDC 2017
CountryAustralia
CityMelbourne
Period12/12/1715/12/17
Internet address

Fingerprint

Quadratic programming
Local Convergence
Quadratic Programming
Approximation
Nonlinear Optimization
Nonlinear Problem
Guarantee
Optimization Problem
Numerical Examples
Costs

Cite this

Nguyen, T. T., Lazar, M., & Butler, H. (2018). A method to guarantee local convergence for sequential quadratic programming with poor Hessian approximation. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 (pp. 3781-3786). Piscataway: Institute of Electrical and Electronics Engineers. DOI: 10.1109/CDC.2017.8264215
Nguyen, Tuan T. ; Lazar, Mircea ; Butler, Hans. / A method to guarantee local convergence for sequential quadratic programming with poor Hessian approximation. 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Piscataway : Institute of Electrical and Electronics Engineers, 2018. pp. 3781-3786
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Nguyen, TT, Lazar, M & Butler, H 2018, A method to guarantee local convergence for sequential quadratic programming with poor Hessian approximation. in 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Institute of Electrical and Electronics Engineers, Piscataway, pp. 3781-3786, 56th IEEE Conference on Decision and Control (CDC 2017), Melbourne, Australia, 12/12/17. DOI: 10.1109/CDC.2017.8264215

A method to guarantee local convergence for sequential quadratic programming with poor Hessian approximation. / Nguyen, Tuan T.; Lazar, Mircea; Butler, Hans.

2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Piscataway : Institute of Electrical and Electronics Engineers, 2018. p. 3781-3786.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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N2 - Sequential Quadratic Programming (SQP) is a powerful class of algorithms for solving nonlinear optimization problems. Local convergence of SQP algorithms is guaranteed when the Hessian approximation used in each Quadratic Programming subproblem is close to the true Hessian. However, a good Hessian approximation can be expensive to compute. Low cost Hessian approximations only guarantee local convergence under some assumptions, which are not always satisfied in practice. To address this problem, this paper proposes a simple method to guarantee local convergence for SQP with poor Hessian approximation. The effectiveness of the proposed algorithm is demonstrated in a numerical example.

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Nguyen TT, Lazar M, Butler H. A method to guarantee local convergence for sequential quadratic programming with poor Hessian approximation. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Piscataway: Institute of Electrical and Electronics Engineers. 2018. p. 3781-3786. Available from, DOI: 10.1109/CDC.2017.8264215