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

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

Résultats de recherche: Papier de travailArticle de travail

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.
langueAnglais
EditeurArxiv
Volume1705.07285
étatSoumis - 17 mai 2017

Empreinte digitale

Nonconvex Optimization
Constrained optimization
Constrained Optimization
Optimality
Criticality
Higher Order
Evaluation
Penalization
Nonlinear Optimization
Critical point
Necessary Conditions

mots-clés

    Citer ceci

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    Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization. / Cartis, Coralia; Gould, N. I. M.; Toint, Philippe.

    Arxiv, 2017.

    Résultats de recherche: Papier de travailArticle de travail

    TY - UNPB

    T1 - Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization

    AU - Cartis,Coralia

    AU - Gould,N. I. M.

    AU - Toint,Philippe

    PY - 2017/5/17

    Y1 - 2017/5/17

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

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

    KW - complexity theory

    KW - nonlinear optimization

    KW - optimality conditions

    KW - High-order models

    M3 - Working paper

    VL - 1705.07285

    BT - Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization

    PB - Arxiv

    ER -