Second-order optimality conditions for nonlinear programs and mathematical programs

It is well known that second-order information is a basic tool notably in optimality conditions and numerical algorithms. In this work, we present a generalization of optimality conditions to strongly convex functions of order γ with the help of first- and second-order approximations derived from (O...

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Detalles Bibliográficos
Autor principal: Daidai, Ikram
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5591379/
https://www.ncbi.nlm.nih.gov/pubmed/28955151
http://dx.doi.org/10.1186/s13660-017-1487-8
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author Daidai, Ikram
author_facet Daidai, Ikram
author_sort Daidai, Ikram
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description It is well known that second-order information is a basic tool notably in optimality conditions and numerical algorithms. In this work, we present a generalization of optimality conditions to strongly convex functions of order γ with the help of first- and second-order approximations derived from (Optimization 40(3):229-246, 2011) and we study their characterization. Further, we give an example of such a function that arises quite naturally in nonlinear analysis and optimization. An extension of Newton’s method is also given and proved to solve Euler equation with second-order approximation data.
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spelling pubmed-55913792017-09-25 Second-order optimality conditions for nonlinear programs and mathematical programs Daidai, Ikram J Inequal Appl Research It is well known that second-order information is a basic tool notably in optimality conditions and numerical algorithms. In this work, we present a generalization of optimality conditions to strongly convex functions of order γ with the help of first- and second-order approximations derived from (Optimization 40(3):229-246, 2011) and we study their characterization. Further, we give an example of such a function that arises quite naturally in nonlinear analysis and optimization. An extension of Newton’s method is also given and proved to solve Euler equation with second-order approximation data. Springer International Publishing 2017-09-08 2017 /pmc/articles/PMC5591379/ /pubmed/28955151 http://dx.doi.org/10.1186/s13660-017-1487-8 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Daidai, Ikram
Second-order optimality conditions for nonlinear programs and mathematical programs
title Second-order optimality conditions for nonlinear programs and mathematical programs
title_full Second-order optimality conditions for nonlinear programs and mathematical programs
title_fullStr Second-order optimality conditions for nonlinear programs and mathematical programs
title_full_unstemmed Second-order optimality conditions for nonlinear programs and mathematical programs
title_short Second-order optimality conditions for nonlinear programs and mathematical programs
title_sort second-order optimality conditions for nonlinear programs and mathematical programs
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5591379/
https://www.ncbi.nlm.nih.gov/pubmed/28955151
http://dx.doi.org/10.1186/s13660-017-1487-8
work_keys_str_mv AT daidaiikram secondorderoptimalityconditionsfornonlinearprogramsandmathematicalprograms

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