Optimality of orders one to three and beyond: Characterization and evaluation complexity in constrained nonconvex optimization

Coralia Cartis; N. I. M. Gould; Philippe Toint

doi:2018_TointPh_Article

Optimality of orders one to three and beyond: Characterization and evaluation complexity in constrained nonconvex optimization

Coralia Cartis, N. I. M. Gould, Philippe Toint

Namur Institute for Complex Systems

Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

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Résumé

Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second- and third-order criticality and its evaluation complexity is analyzed as a function of the choice (among existing methods) of an inner algorithm for solving subproblems in each of the two phases. The relation between high-order criticality and penalization techniques is finally considered, showing that standard algorithmic approaches will fail if approximate constrained high-order critical points are sought.

langue originale	Anglais
Pages (de - à)	68-94
Nombre de pages	32
journal	Journal of Complexity
Volume	53
Les DOIs	https://doi.org/2018_TointPh_Article
Etat de la publication	Publié - 10 août 2019

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2 Actif

Complexity in nonlinear optimization
TOINT, P., Gould, N. I. M. & Cartis, C.
1/11/08 → …
Projet: Recherche
ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire
SARTENAER, A. & TOINT, P.
1/01/87 → …
Projet: Axe de recherche

3 Discours invité
2 Visite à une institution académique externe
1 Participation à un atelier/workshop, un séminaire, un cours

5th Conference on Numerical Analysis and Optimization
Philippe Toint (Orateur)
6 janv. 2020 → 9 janv. 2020
Activité: Types de Participation ou d'organisation d'un événement › Participation à un atelier/workshop, un séminaire, un cours
Oxford University
Philippe Toint (Chercheur visiteur)
20 nov. 2019 → 6 déc. 2019
Activité: Types de Visite d'une organisation externe › Visite à une institution académique externe
Recent progress in evaluation complexity for nonlinear optimization
Philippe Toint (Orateur)
4 oct. 2019
Activité: Types de discours ou de présentation › Discours invité

Contient cette citation

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title = "Optimality of orders one to three and beyond: Characterization and evaluation complexity in constrained nonconvex optimization",

abstract = "Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second- and third-order criticality and its evaluation complexity is analyzed as a function of the choice (among existing methods) of an inner algorithm for solving subproblems in each of the two phases. The relation between high-order criticality and penalization techniques is finally considered, showing that standard algorithmic approaches will fail if approximate constrained high-order critical points are sought.",

keywords = "Complexity theory, Constrained problems, High-order optimality conditions, Nonlinear optimization",

author = "Coralia Cartis and Gould, {N. I. M.} and Philippe Toint",

note = "Funding Information: The authors would like to thank Oliver Stein for suggesting reference [41] . The work of the second author was supported by EPSRC, United Kingdom grant EP/M025179/1 . The third author acknowledges the support provided by the Belgian Fund for Scientific Research (FNRS) , the Leverhulme Trust (UK) , Balliol College (Oxford, UK) , the Department of Applied Mathematics of the Hong Kong Polytechnic University , ENSEEIHT (Toulouse, France) and INDAM (Florence, Italy) . Thanks are also due to a thoughtful referee whose patience and perceptive comments have helped to significantly improve the manuscript. Publisher Copyright: {\textcopyright} 2018 Elsevier Inc. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",

year = "2019",

month = aug,

day = "10",

doi = "2018_TointPh_Article",

language = "English",

volume = "53",

pages = "68--94",

journal = "Journal of Complexity",

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T2 - Characterization and evaluation complexity in constrained nonconvex optimization

AU - Cartis, Coralia

AU - Gould, N. I. M.

AU - Toint, Philippe

N1 - Funding Information: The authors would like to thank Oliver Stein for suggesting reference [41] . The work of the second author was supported by EPSRC, United Kingdom grant EP/M025179/1 . The third author acknowledges the support provided by the Belgian Fund for Scientific Research (FNRS) , the Leverhulme Trust (UK) , Balliol College (Oxford, UK) , the Department of Applied Mathematics of the Hong Kong Polytechnic University , ENSEEIHT (Toulouse, France) and INDAM (Florence, Italy) . Thanks are also due to a thoughtful referee whose patience and perceptive comments have helped to significantly improve the manuscript. Publisher Copyright: © 2018 Elsevier Inc. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019/8/10

Y1 - 2019/8/10

N2 - Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second- and third-order criticality and its evaluation complexity is analyzed as a function of the choice (among existing methods) of an inner algorithm for solving subproblems in each of the two phases. The relation between high-order criticality and penalization techniques is finally considered, showing that standard algorithmic approaches will fail if approximate constrained high-order critical points are sought.

AB - Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second- and third-order criticality and its evaluation complexity is analyzed as a function of the choice (among existing methods) of an inner algorithm for solving subproblems in each of the two phases. The relation between high-order criticality and penalization techniques is finally considered, showing that standard algorithmic approaches will fail if approximate constrained high-order critical points are sought.

KW - Complexity theory

KW - Constrained problems

KW - High-order optimality conditions

KW - Nonlinear optimization

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JO - Journal of Complexity

JF - Journal of Complexity

SN - 0885-064X

ER -

Optimality of orders one to three and beyond: Characterization and evaluation complexity in constrained nonconvex optimization

Résumé

Accès au document

Autres fichiers et liens

Complexity in nonlinear optimization

ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire

5th Conference on Numerical Analysis and Optimization

Oxford University

Recent progress in evaluation complexity for nonlinear optimization

Contient cette citation