Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-12

AUTHORS

Shougui Zhang, Yueyue Yan, Ruisheng Ran

ABSTRACT

A semismooth Newton method, based on variational inequalities and generalized derivative, is designed and analysed for unilateral contact problem between two membranes. The problem is first formulated as a corresponding regularized problem with a nonlinear function, which can be solved by the semismooth Newton method. We prove the convergence of the method in the function space. To improve the performance of the semismooth Newton method, we use the path-following method to adjust the parameter automatically. Finally, some numerical results are presented to illustrate the performance of the proposed method. More... »

PAGES

1

References to SciGraph publications

  • 2008-10. Semi-smooth Newton methods for the Signorini problem in APPLICATIONS OF MATHEMATICS
  • 2012-04. Path-following for optimal control of stationary variational inequalities in COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
  • 2016-10. Optimal control of the two membranes problem: optimality conditions in JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
  • 2017-12. A smoothing inexact Newton method for variational inequalities with nonlinear constraints in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1186/s13660-019-1955-4

    DOI

    http://dx.doi.org/10.1186/s13660-019-1955-4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1111158833

    PUBMED

    https://www.ncbi.nlm.nih.gov/pubmed/30662247


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0103", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Numerical and Computational Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Chongqing Normal University", 
              "id": "https://www.grid.ac/institutes/grid.411575.3", 
              "name": [
                "School of Mathematical Sciences, Chongqing Normal University, Chongqing, P.R. China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Zhang", 
            "givenName": "Shougui", 
            "id": "sg:person.015764772567.51", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015764772567.51"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Chongqing Normal University", 
              "id": "https://www.grid.ac/institutes/grid.411575.3", 
              "name": [
                "School of Mathematical Sciences, Chongqing Normal University, Chongqing, P.R. China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Yan", 
            "givenName": "Yueyue", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Chongqing Normal University", 
              "id": "https://www.grid.ac/institutes/grid.411575.3", 
              "name": [
                "College of Computer and Information Science, Chongqing Normal University, Chongqing, P.R. China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Ran", 
            "givenName": "Ruisheng", 
            "id": "sg:person.07467321600.71", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07467321600.71"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1081/pde-200044490", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1005680153"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10589-011-9400-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009614651", 
              "https://doi.org/10.1007/s10589-011-9400-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cam.2006.04.017", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010442754"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1155/s0161171201004823", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023860860"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s12190-015-0939-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025004956", 
              "https://doi.org/10.1007/s12190-015-0939-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0167-6911(03)00156-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029650762"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0167-6911(03)00156-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029650762"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cam.2010.08.012", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032236383"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cam.2015.06.010", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032858886"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4208/nmtma.2015.w08si", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033603137"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/01630563.2012.716805", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034150739"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10492-008-0036-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047202338", 
              "https://doi.org/10.1007/s10492-008-0036-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1051/m2an/2008041", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1057032198"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1051/m2an:2003021", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1057033019"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1051/m2an:2005036", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1057033150"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1051/m2an:2005036", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1057033150"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1051/mmnp/20094102", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1057046013"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1093/imanum/drr003", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059689677"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/s1052623401383558", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062883243"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1186/s13660-017-1433-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1090587849", 
              "https://doi.org/10.1186/s13660-017-1433-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1186/s13660-017-1433-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1090587849", 
              "https://doi.org/10.1186/s13660-017-1433-9"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2019-12", 
        "datePublishedReg": "2019-12-01", 
        "description": "A semismooth Newton method, based on variational inequalities and generalized derivative, is designed and analysed for unilateral contact problem between two membranes. The problem is first formulated as a corresponding regularized problem with a nonlinear function, which can be solved by the semismooth Newton method. We prove the convergence of the method in the function space. To improve the performance of the semismooth Newton method, we use the path-following method to adjust the parameter automatically. Finally, some numerical results are presented to illustrate the performance of the proposed method.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1186/s13660-019-1955-4", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1136856", 
            "issn": [
              "1025-5834", 
              "1029-242X"
            ], 
            "name": "Journal of Inequalities and Applications", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "2019"
          }
        ], 
        "name": "Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem", 
        "pagination": "1", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "574885a14c5548f872ae276beb1de81da2dc97d4612586ea4617daf5f4e1da07"
            ]
          }, 
          {
            "name": "pubmed_id", 
            "type": "PropertyValue", 
            "value": [
              "30662247"
            ]
          }, 
          {
            "name": "nlm_unique_id", 
            "type": "PropertyValue", 
            "value": [
              "101697598"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1186/s13660-019-1955-4"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1111158833"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1186/s13660-019-1955-4", 
          "https://app.dimensions.ai/details/publication/pub.1111158833"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T08:43", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000322_0000000322/records_64988_00000000.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1186%2Fs13660-019-1955-4"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1186/s13660-019-1955-4'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1186/s13660-019-1955-4'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1186/s13660-019-1955-4'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1186/s13660-019-1955-4'


     

    This table displays all metadata directly associated to this object as RDF triples.

    141 TRIPLES      21 PREDICATES      47 URIs      21 LITERALS      9 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1186/s13660-019-1955-4 schema:about anzsrc-for:01
    2 anzsrc-for:0103
    3 schema:author Nc484f33bb1224a459805798c57a951eb
    4 schema:citation sg:pub.10.1007/s10492-008-0036-7
    5 sg:pub.10.1007/s10589-011-9400-8
    6 sg:pub.10.1007/s12190-015-0939-x
    7 sg:pub.10.1186/s13660-017-1433-9
    8 https://doi.org/10.1016/j.cam.2006.04.017
    9 https://doi.org/10.1016/j.cam.2010.08.012
    10 https://doi.org/10.1016/j.cam.2015.06.010
    11 https://doi.org/10.1016/s0167-6911(03)00156-7
    12 https://doi.org/10.1051/m2an/2008041
    13 https://doi.org/10.1051/m2an:2003021
    14 https://doi.org/10.1051/m2an:2005036
    15 https://doi.org/10.1051/mmnp/20094102
    16 https://doi.org/10.1080/01630563.2012.716805
    17 https://doi.org/10.1081/pde-200044490
    18 https://doi.org/10.1093/imanum/drr003
    19 https://doi.org/10.1137/s1052623401383558
    20 https://doi.org/10.1155/s0161171201004823
    21 https://doi.org/10.4208/nmtma.2015.w08si
    22 schema:datePublished 2019-12
    23 schema:datePublishedReg 2019-12-01
    24 schema:description A semismooth Newton method, based on variational inequalities and generalized derivative, is designed and analysed for unilateral contact problem between two membranes. The problem is first formulated as a corresponding regularized problem with a nonlinear function, which can be solved by the semismooth Newton method. We prove the convergence of the method in the function space. To improve the performance of the semismooth Newton method, we use the path-following method to adjust the parameter automatically. Finally, some numerical results are presented to illustrate the performance of the proposed method.
    25 schema:genre research_article
    26 schema:inLanguage en
    27 schema:isAccessibleForFree true
    28 schema:isPartOf N59144b901362406ab44dd741b7b6d070
    29 Nf226825ee8c94db5a5d83da5869c7ab9
    30 sg:journal.1136856
    31 schema:name Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem
    32 schema:pagination 1
    33 schema:productId N336b74b5b82b4ad5b601d6ead74339e9
    34 N64b3fd23546d432f8f5ffcbd71d05923
    35 N84bb42fe67974a30a34e3ae0f37f3ff0
    36 N85daf7aa08bf47e39e672c9f735441ed
    37 N900e7ed4da5144f8bb175229242ab88c
    38 schema:sameAs https://app.dimensions.ai/details/publication/pub.1111158833
    39 https://doi.org/10.1186/s13660-019-1955-4
    40 schema:sdDatePublished 2019-04-11T08:43
    41 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    42 schema:sdPublisher N32b12d8e0b684330902748762c7f7661
    43 schema:url https://link.springer.com/10.1186%2Fs13660-019-1955-4
    44 sgo:license sg:explorer/license/
    45 sgo:sdDataset articles
    46 rdf:type schema:ScholarlyArticle
    47 N32b12d8e0b684330902748762c7f7661 schema:name Springer Nature - SN SciGraph project
    48 rdf:type schema:Organization
    49 N336b74b5b82b4ad5b601d6ead74339e9 schema:name dimensions_id
    50 schema:value pub.1111158833
    51 rdf:type schema:PropertyValue
    52 N59144b901362406ab44dd741b7b6d070 schema:volumeNumber 2019
    53 rdf:type schema:PublicationVolume
    54 N64b3fd23546d432f8f5ffcbd71d05923 schema:name doi
    55 schema:value 10.1186/s13660-019-1955-4
    56 rdf:type schema:PropertyValue
    57 N7f14ecdd33414de8b1bdac05d73af60f rdf:first sg:person.07467321600.71
    58 rdf:rest rdf:nil
    59 N84bb42fe67974a30a34e3ae0f37f3ff0 schema:name pubmed_id
    60 schema:value 30662247
    61 rdf:type schema:PropertyValue
    62 N85daf7aa08bf47e39e672c9f735441ed schema:name readcube_id
    63 schema:value 574885a14c5548f872ae276beb1de81da2dc97d4612586ea4617daf5f4e1da07
    64 rdf:type schema:PropertyValue
    65 N8cf11d8bfa3749efba0803a1c0540595 rdf:first Nebd937be2927483297da9afcb958ecee
    66 rdf:rest N7f14ecdd33414de8b1bdac05d73af60f
    67 N900e7ed4da5144f8bb175229242ab88c schema:name nlm_unique_id
    68 schema:value 101697598
    69 rdf:type schema:PropertyValue
    70 Nc484f33bb1224a459805798c57a951eb rdf:first sg:person.015764772567.51
    71 rdf:rest N8cf11d8bfa3749efba0803a1c0540595
    72 Nebd937be2927483297da9afcb958ecee schema:affiliation https://www.grid.ac/institutes/grid.411575.3
    73 schema:familyName Yan
    74 schema:givenName Yueyue
    75 rdf:type schema:Person
    76 Nf226825ee8c94db5a5d83da5869c7ab9 schema:issueNumber 1
    77 rdf:type schema:PublicationIssue
    78 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    79 schema:name Mathematical Sciences
    80 rdf:type schema:DefinedTerm
    81 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
    82 schema:name Numerical and Computational Mathematics
    83 rdf:type schema:DefinedTerm
    84 sg:journal.1136856 schema:issn 1025-5834
    85 1029-242X
    86 schema:name Journal of Inequalities and Applications
    87 rdf:type schema:Periodical
    88 sg:person.015764772567.51 schema:affiliation https://www.grid.ac/institutes/grid.411575.3
    89 schema:familyName Zhang
    90 schema:givenName Shougui
    91 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015764772567.51
    92 rdf:type schema:Person
    93 sg:person.07467321600.71 schema:affiliation https://www.grid.ac/institutes/grid.411575.3
    94 schema:familyName Ran
    95 schema:givenName Ruisheng
    96 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07467321600.71
    97 rdf:type schema:Person
    98 sg:pub.10.1007/s10492-008-0036-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047202338
    99 https://doi.org/10.1007/s10492-008-0036-7
    100 rdf:type schema:CreativeWork
    101 sg:pub.10.1007/s10589-011-9400-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009614651
    102 https://doi.org/10.1007/s10589-011-9400-8
    103 rdf:type schema:CreativeWork
    104 sg:pub.10.1007/s12190-015-0939-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1025004956
    105 https://doi.org/10.1007/s12190-015-0939-x
    106 rdf:type schema:CreativeWork
    107 sg:pub.10.1186/s13660-017-1433-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1090587849
    108 https://doi.org/10.1186/s13660-017-1433-9
    109 rdf:type schema:CreativeWork
    110 https://doi.org/10.1016/j.cam.2006.04.017 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010442754
    111 rdf:type schema:CreativeWork
    112 https://doi.org/10.1016/j.cam.2010.08.012 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032236383
    113 rdf:type schema:CreativeWork
    114 https://doi.org/10.1016/j.cam.2015.06.010 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032858886
    115 rdf:type schema:CreativeWork
    116 https://doi.org/10.1016/s0167-6911(03)00156-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029650762
    117 rdf:type schema:CreativeWork
    118 https://doi.org/10.1051/m2an/2008041 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057032198
    119 rdf:type schema:CreativeWork
    120 https://doi.org/10.1051/m2an:2003021 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057033019
    121 rdf:type schema:CreativeWork
    122 https://doi.org/10.1051/m2an:2005036 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057033150
    123 rdf:type schema:CreativeWork
    124 https://doi.org/10.1051/mmnp/20094102 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057046013
    125 rdf:type schema:CreativeWork
    126 https://doi.org/10.1080/01630563.2012.716805 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034150739
    127 rdf:type schema:CreativeWork
    128 https://doi.org/10.1081/pde-200044490 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005680153
    129 rdf:type schema:CreativeWork
    130 https://doi.org/10.1093/imanum/drr003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059689677
    131 rdf:type schema:CreativeWork
    132 https://doi.org/10.1137/s1052623401383558 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062883243
    133 rdf:type schema:CreativeWork
    134 https://doi.org/10.1155/s0161171201004823 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023860860
    135 rdf:type schema:CreativeWork
    136 https://doi.org/10.4208/nmtma.2015.w08si schema:sameAs https://app.dimensions.ai/details/publication/pub.1033603137
    137 rdf:type schema:CreativeWork
    138 https://www.grid.ac/institutes/grid.411575.3 schema:alternateName Chongqing Normal University
    139 schema:name College of Computer and Information Science, Chongqing Normal University, Chongqing, P.R. China
    140 School of Mathematical Sciences, Chongqing Normal University, Chongqing, P.R. China
    141 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...