Stabilized Optimization Via an NCL Algorithm

Ding Ma; Kenneth L. Judd; Dominique Orban; Michael A. Saunders

doi:10.1007/978-3-319-90026-1_8

Stabilized Optimization Via an NCL Algorithm

Ding Ma
, Kenneth L. Judd
, Dominique Orban
, Michael A. Saunders^*

^*Corresponding author for this work

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

4 Citations (Scopus)

Abstract

For optimization problems involving many nonlinear inequality constraints, we extend the bound-constrained (BCL) and linearly constrained (LCL) augmented Lagrangian approaches of LANCELOT and MINOS to an algorithm that solves a sequence of nonlinearly constrained augmented Lagrangian subproblems whose nonlinear constraints satisfy the LICQ everywhere. The NCL algorithm is implemented in AMPL and tested on large instances of a tax policy model that could not be solved directly by the state-of-the-art solvers that we tested, because of singularity in the Jacobian of the active constraints. Algorithm NCL with IPOPT as subproblem solver proves to be effective, with IPOPT using second derivatives and successfully warm starting each subproblem.

Original language	English
Title of host publication	Numerical Analysis and Optimization
Editors	Mehiddin Al-Baali, Lucio Grandinetti, Anton Purnama
Publisher	Springer Nature
Pages	173-191
ISBN (Electronic)	9783319900261
ISBN (Print)	9783319900254
DOIs	https://doi.org/10.1007/978-3-319-90026-1_8
Publication status	Published - 2018
Externally published	Yes
Event	4th International Conference of Numerical Analysis and Optimization (NAO-IV 2017) - Muscat, Oman Duration: 2 Jan 2017 → 5 Jan 2017

Publication series

Name	Springer Proceedings in Mathematics & Statistics
Volume	235
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	4th International Conference of Numerical Analysis and Optimization (NAO-IV 2017)
Abbreviated title	NAO-IV 2017
Place	Oman
City	Muscat
Period	2/01/17 → 5/01/17

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 17 Partnerships for the Goals

Research Keywords

Stabilized optimization
LICQ
Augmented Lagrangian
BCL NCL
Interior method
Warm start

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10.1007/978-3-319-90026-1_8

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@inproceedings{98c057ace2f046f38f46712768188c0e,

title = "Stabilized Optimization Via an NCL Algorithm",

abstract = "For optimization problems involving many nonlinear inequality constraints, we extend the bound-constrained (BCL) and linearly constrained (LCL) augmented Lagrangian approaches of LANCELOT and MINOS to an algorithm that solves a sequence of nonlinearly constrained augmented Lagrangian subproblems whose nonlinear constraints satisfy the LICQ everywhere. The NCL algorithm is implemented in AMPL and tested on large instances of a tax policy model that could not be solved directly by the state-of-the-art solvers that we tested, because of singularity in the Jacobian of the active constraints. Algorithm NCL with IPOPT as subproblem solver proves to be effective, with IPOPT using second derivatives and successfully warm starting each subproblem.",

keywords = "Stabilized optimization, LICQ, Augmented Lagrangian, BCL NCL, Interior method, Warm start",

author = "Ding Ma and Judd, \{Kenneth L.\} and Dominique Orban and Saunders, \{Michael A.\}",

year = "2018",

doi = "10.1007/978-3-319-90026-1\_8",

language = "English",

isbn = "9783319900254",

series = "Springer Proceedings in Mathematics \& Statistics",

publisher = "Springer Nature",

pages = "173--191",

editor = "Mehiddin Al-Baali and Lucio Grandinetti and Anton Purnama",

booktitle = "Numerical Analysis and Optimization",

note = "4th International Conference of Numerical Analysis and Optimization (NAO-IV 2017), NAO-IV 2017 ; Conference date: 02-01-2017 Through 05-01-2017",

}

Ma, D, Judd, KL, Orban, D & Saunders, MA 2018, Stabilized Optimization Via an NCL Algorithm. in M Al-Baali, L Grandinetti & A Purnama (eds), Numerical Analysis and Optimization. Springer Proceedings in Mathematics & Statistics, vol. 235, Springer Nature, pp. 173-191, 4th International Conference of Numerical Analysis and Optimization (NAO-IV 2017), Muscat, Oman, 2/01/17. https://doi.org/10.1007/978-3-319-90026-1_8

Stabilized Optimization Via an NCL Algorithm. / Ma, Ding; Judd, Kenneth L.; Orban, Dominique et al.
Numerical Analysis and Optimization. ed. / Mehiddin Al-Baali; Lucio Grandinetti; Anton Purnama. Springer Nature, 2018. p. 173-191 (Springer Proceedings in Mathematics & Statistics; Vol. 235).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Stabilized Optimization Via an NCL Algorithm

AU - Ma, Ding

AU - Judd, Kenneth L.

AU - Orban, Dominique

AU - Saunders, Michael A.

PY - 2018

Y1 - 2018

N2 - For optimization problems involving many nonlinear inequality constraints, we extend the bound-constrained (BCL) and linearly constrained (LCL) augmented Lagrangian approaches of LANCELOT and MINOS to an algorithm that solves a sequence of nonlinearly constrained augmented Lagrangian subproblems whose nonlinear constraints satisfy the LICQ everywhere. The NCL algorithm is implemented in AMPL and tested on large instances of a tax policy model that could not be solved directly by the state-of-the-art solvers that we tested, because of singularity in the Jacobian of the active constraints. Algorithm NCL with IPOPT as subproblem solver proves to be effective, with IPOPT using second derivatives and successfully warm starting each subproblem.

AB - For optimization problems involving many nonlinear inequality constraints, we extend the bound-constrained (BCL) and linearly constrained (LCL) augmented Lagrangian approaches of LANCELOT and MINOS to an algorithm that solves a sequence of nonlinearly constrained augmented Lagrangian subproblems whose nonlinear constraints satisfy the LICQ everywhere. The NCL algorithm is implemented in AMPL and tested on large instances of a tax policy model that could not be solved directly by the state-of-the-art solvers that we tested, because of singularity in the Jacobian of the active constraints. Algorithm NCL with IPOPT as subproblem solver proves to be effective, with IPOPT using second derivatives and successfully warm starting each subproblem.

KW - Stabilized optimization

KW - LICQ

KW - Augmented Lagrangian

KW - BCL NCL

KW - Interior method

KW - Warm start

UR - https://www.scopus.com/pages/publications/85048243659

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85048243659&origin=recordpage

U2 - 10.1007/978-3-319-90026-1_8

DO - 10.1007/978-3-319-90026-1_8

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 9783319900254

T3 - Springer Proceedings in Mathematics & Statistics

SP - 173

EP - 191

BT - Numerical Analysis and Optimization

A2 - Al-Baali, Mehiddin

A2 - Grandinetti, Lucio

A2 - Purnama, Anton

PB - Springer Nature

T2 - 4th International Conference of Numerical Analysis and Optimization (NAO-IV 2017)

Y2 - 2 January 2017 through 5 January 2017

ER -

Stabilized Optimization Via an NCL Algorithm

Abstract

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Conference

UN SDGs

Research Keywords

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