Generalized Gerstewitz’s Functions and Vector Variational Principle for ε-Efficient Solutions in the Sense of Németh View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03

AUTHORS

Jing Hui Qiu

ABSTRACT

In this paper, we first generalize Gerstewitz’s functions from a single positive vector to a subset of the positive cone. Then, we establish a partial order principle, which is indeed a variant of the pre-order principle [Qiu, J. H.: A pre-order principle and set-valued Ekeland variational principle. J. Math. Anal. Appl., 419, 904–937 (2014)]. By using the generalized Gerstewitz’s functions and the partial order principle, we obtain a vector EVP for ε-efficient solutions in the sense of Németh, which essentially improves the earlier results by completely removing a usual assumption for boundedness of the objective function. From this, we also deduce several special vector EVPs, which improve and generalize the related known results. More... »

PAGES

1-24

References to SciGraph publications

  • 1996-05. On variational principles, level sets, well-posedness, and ∈-solutions in vector optimization in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1998-12. A unified approach to the existing three types of variational principles for vector valued functions in MATHEMATICAL METHODS OF OPERATIONS RESEARCH
  • 2010-04. Relative Pareto minimizers for multiobjective problems: existence and optimality conditions in MATHEMATICAL PROGRAMMING
  • 2013-11. Versions of Ekeland’s variational principle involving set perturbations in JOURNAL OF GLOBAL OPTIMIZATION
  • 1996. The Ekeland’s Principle and the Pareto ε-Efficiency in MULTI-OBJECTIVE PROGRAMMING AND GOAL PROGRAMMING
  • 2009-12. Vector variational principle in ARCHIV DER MATHEMATIK
  • 2013-09. A general vectorial Ekeland’s variational principle with a P-distance in ACTA MATHEMATICA SINICA, ENGLISH SERIES
  • 2000-07. Generalized Variational Principle and Vector Optimization in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1963. Linear Topological Spaces in NONE
  • 2004-06. Proper Efficiency in Vector Optimization on Real Linear Spaces in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2015-08. Sequentially lower complete spaces and Ekeland’s variational principle in ACTA MATHEMATICA SINICA, ENGLISH SERIES
  • 2006-08. On Approximate Efficiency in Multiobjective Programming in MATHEMATICAL METHODS OF OPERATIONS RESEARCH
  • 2005-01. Some Variants of the Ekeland Variational Principle for a Set-Valued Map in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1997. Foundations of Mathematical Optimization, Convex Analysis without Linearity in NONE
  • 2012-04. On Ha’s version of set-valued Ekeland’s variational principle in ACTA MATHEMATICA SINICA, ENGLISH SERIES
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10114-018-7159-x

    DOI

    http://dx.doi.org/10.1007/s10114-018-7159-x

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1110668337


    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/2008/0306", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Physical Chemistry (incl. Structural)", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/03", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Chemical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Soochow University", 
              "id": "https://www.grid.ac/institutes/grid.263761.7", 
              "name": [
                "School of Mathematical Sciences, Soochow University, 215006, Suzhou, P. R. China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Qiu", 
            "givenName": "Jing Hui", 
            "id": "sg:person.015202174441.44", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015202174441.44"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/s10107-008-0249-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001666377", 
              "https://doi.org/10.1007/s10107-008-0249-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10107-008-0249-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001666377", 
              "https://doi.org/10.1007/s10107-008-0249-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1002266580", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-94-017-1588-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002266580", 
              "https://doi.org/10.1007/978-94-017-1588-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-94-017-1588-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002266580", 
              "https://doi.org/10.1007/978-94-017-1588-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10898-012-9983-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002364427", 
              "https://doi.org/10.1007/s10898-012-9983-3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0273-0979-1979-14595-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003139392"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10114-011-0294-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003216092", 
              "https://doi.org/10.1007/s10114-011-0294-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jmaa.2014.05.027", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003219716"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10957-004-6472-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003575664", 
              "https://doi.org/10.1007/s10957-004-6472-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10114-015-4541-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004601583", 
              "https://doi.org/10.1007/s10114-015-4541-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/02331934.2010.522712", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007726467"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s001860050032", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008319736", 
              "https://doi.org/10.1007/s001860050032"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0362-546x(98)00255-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1008560415"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.na.2009.03.034", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009389647"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0362-546x(86)90126-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009491213"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jmaa.2008.06.020", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010217204"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0002-9939-97-03864-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012166030"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02192533", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015717068", 
              "https://doi.org/10.1007/bf02192533"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02192533", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015717068", 
              "https://doi.org/10.1007/bf02192533"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.na.2005.04.011", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017093300"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.na.2005.04.011", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1017093300"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/02331939208843815", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018896815"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1018897175", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-662-41914-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018897175", 
              "https://doi.org/10.1007/978-3-662-41914-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-662-41914-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018897175", 
              "https://doi.org/10.1007/978-3-662-41914-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0002-9939-00-05717-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019577543"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1006/jmaa.2001.7709", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019888957"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1004619426652", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019934147", 
              "https://doi.org/10.1023/a:1004619426652"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jmaa.2012.12.072", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023719776"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0022-247x(74)90025-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024814013"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0362-546x(02)00103-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029380498"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0362-546x(02)00103-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1029380498"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10114-013-2284-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1031156917", 
              "https://doi.org/10.1007/s10114-013-2284-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0252-9602(12)60172-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036493151"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-642-87561-8_12", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036656617", 
              "https://doi.org/10.1007/978-3-642-87561-8_12"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/b:jota.0000037602.13941.ed", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039210584", 
              "https://doi.org/10.1023/b:jota.0000037602.13941.ed"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00186-006-0078-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041004172", 
              "https://doi.org/10.1007/s00186-006-0078-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00186-006-0078-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1041004172", 
              "https://doi.org/10.1007/s00186-006-0078-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00013-009-0072-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043001860", 
              "https://doi.org/10.1007/s00013-009-0072-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00013-009-0072-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043001860", 
              "https://doi.org/10.1007/s00013-009-0072-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00013-009-0072-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043001860", 
              "https://doi.org/10.1007/s00013-009-0072-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jmaa.2008.04.055", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044182609"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0377-2217(02)00444-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044439244"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0377-2217(02)00444-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044439244"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4134/bkms.2002.39.4.535", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044547227"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jmaa.2010.09.014", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050612852"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/05062648x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062846076"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/060658989", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062849346"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/060672868", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062849800"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/090760660", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062856380"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1137/110824115", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062864616"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/5021", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1098867970"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2019-03", 
        "datePublishedReg": "2019-03-01", 
        "description": "In this paper, we first generalize Gerstewitz\u2019s functions from a single positive vector to a subset of the positive cone. Then, we establish a partial order principle, which is indeed a variant of the pre-order principle [Qiu, J. H.: A pre-order principle and set-valued Ekeland variational principle. J. Math. Anal. Appl., 419, 904\u2013937 (2014)]. By using the generalized Gerstewitz\u2019s functions and the partial order principle, we obtain a vector EVP for \u03b5-efficient solutions in the sense of N\u00e9meth, which essentially improves the earlier results by completely removing a usual assumption for boundedness of the objective function. From this, we also deduce several special vector EVPs, which improve and generalize the related known results.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s10114-018-7159-x", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1040372", 
            "issn": [
              "1439-8516", 
              "1439-7617"
            ], 
            "name": "Acta Mathematica Sinica, English Series", 
            "type": "Periodical"
          }
        ], 
        "name": "Generalized Gerstewitz\u2019s Functions and Vector Variational Principle for \u03b5-Efficient Solutions in the Sense of N\u00e9meth", 
        "pagination": "1-24", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "20824a6ab1e6e4e0e5478ffaa5047a69f3cda86ea2a50c7b5d4c6941ef76080c"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s10114-018-7159-x"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1110668337"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s10114-018-7159-x", 
          "https://app.dimensions.ai/details/publication/pub.1110668337"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T08:24", 
        "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/v90/0000000296_0000000296/records_57222_00000000.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs10114-018-7159-x"
      }
    ]
     

    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.10.1007/s10114-018-7159-x'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10114-018-7159-x'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10114-018-7159-x'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10114-018-7159-x'


     

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

    197 TRIPLES      21 PREDICATES      68 URIs      17 LITERALS      5 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s10114-018-7159-x schema:about anzsrc-for:03
    2 anzsrc-for:0306
    3 schema:author N7c3c4e143cd04d7b95d7216c6bfcbc52
    4 schema:citation sg:pub.10.1007/978-3-642-87561-8_12
    5 sg:pub.10.1007/978-3-662-41914-4
    6 sg:pub.10.1007/978-94-017-1588-1
    7 sg:pub.10.1007/bf02192533
    8 sg:pub.10.1007/s00013-009-0072-x
    9 sg:pub.10.1007/s00186-006-0078-0
    10 sg:pub.10.1007/s001860050032
    11 sg:pub.10.1007/s10107-008-0249-2
    12 sg:pub.10.1007/s10114-011-0294-2
    13 sg:pub.10.1007/s10114-013-2284-z
    14 sg:pub.10.1007/s10114-015-4541-9
    15 sg:pub.10.1007/s10898-012-9983-3
    16 sg:pub.10.1007/s10957-004-6472-y
    17 sg:pub.10.1023/a:1004619426652
    18 sg:pub.10.1023/b:jota.0000037602.13941.ed
    19 https://app.dimensions.ai/details/publication/pub.1002266580
    20 https://app.dimensions.ai/details/publication/pub.1018897175
    21 https://doi.org/10.1006/jmaa.2001.7709
    22 https://doi.org/10.1016/0022-247x(74)90025-0
    23 https://doi.org/10.1016/0362-546x(86)90126-4
    24 https://doi.org/10.1016/j.jmaa.2008.04.055
    25 https://doi.org/10.1016/j.jmaa.2008.06.020
    26 https://doi.org/10.1016/j.jmaa.2010.09.014
    27 https://doi.org/10.1016/j.jmaa.2012.12.072
    28 https://doi.org/10.1016/j.jmaa.2014.05.027
    29 https://doi.org/10.1016/j.na.2005.04.011
    30 https://doi.org/10.1016/j.na.2009.03.034
    31 https://doi.org/10.1016/s0252-9602(12)60172-6
    32 https://doi.org/10.1016/s0362-546x(02)00103-7
    33 https://doi.org/10.1016/s0362-546x(98)00255-7
    34 https://doi.org/10.1016/s0377-2217(02)00444-7
    35 https://doi.org/10.1080/02331934.2010.522712
    36 https://doi.org/10.1080/02331939208843815
    37 https://doi.org/10.1090/s0002-9939-00-05717-8
    38 https://doi.org/10.1090/s0002-9939-97-03864-1
    39 https://doi.org/10.1090/s0273-0979-1979-14595-6
    40 https://doi.org/10.1137/05062648x
    41 https://doi.org/10.1137/060658989
    42 https://doi.org/10.1137/060672868
    43 https://doi.org/10.1137/090760660
    44 https://doi.org/10.1137/110824115
    45 https://doi.org/10.1142/5021
    46 https://doi.org/10.4134/bkms.2002.39.4.535
    47 schema:datePublished 2019-03
    48 schema:datePublishedReg 2019-03-01
    49 schema:description In this paper, we first generalize Gerstewitz’s functions from a single positive vector to a subset of the positive cone. Then, we establish a partial order principle, which is indeed a variant of the pre-order principle [Qiu, J. H.: A pre-order principle and set-valued Ekeland variational principle. J. Math. Anal. Appl., 419, 904–937 (2014)]. By using the generalized Gerstewitz’s functions and the partial order principle, we obtain a vector EVP for ε-efficient solutions in the sense of Németh, which essentially improves the earlier results by completely removing a usual assumption for boundedness of the objective function. From this, we also deduce several special vector EVPs, which improve and generalize the related known results.
    50 schema:genre research_article
    51 schema:inLanguage en
    52 schema:isAccessibleForFree false
    53 schema:isPartOf sg:journal.1040372
    54 schema:name Generalized Gerstewitz’s Functions and Vector Variational Principle for ε-Efficient Solutions in the Sense of Németh
    55 schema:pagination 1-24
    56 schema:productId N2bd7d4c7d8344880bd3499f3b3c81632
    57 N9f847387f9e941b78847d41f03362006
    58 Nb72d35503a634d11bf0474e4d85d1a47
    59 schema:sameAs https://app.dimensions.ai/details/publication/pub.1110668337
    60 https://doi.org/10.1007/s10114-018-7159-x
    61 schema:sdDatePublished 2019-04-11T08:24
    62 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    63 schema:sdPublisher N688b4464457944e2a36b4bd20d4a500d
    64 schema:url https://link.springer.com/10.1007%2Fs10114-018-7159-x
    65 sgo:license sg:explorer/license/
    66 sgo:sdDataset articles
    67 rdf:type schema:ScholarlyArticle
    68 N2bd7d4c7d8344880bd3499f3b3c81632 schema:name dimensions_id
    69 schema:value pub.1110668337
    70 rdf:type schema:PropertyValue
    71 N688b4464457944e2a36b4bd20d4a500d schema:name Springer Nature - SN SciGraph project
    72 rdf:type schema:Organization
    73 N7c3c4e143cd04d7b95d7216c6bfcbc52 rdf:first sg:person.015202174441.44
    74 rdf:rest rdf:nil
    75 N9f847387f9e941b78847d41f03362006 schema:name readcube_id
    76 schema:value 20824a6ab1e6e4e0e5478ffaa5047a69f3cda86ea2a50c7b5d4c6941ef76080c
    77 rdf:type schema:PropertyValue
    78 Nb72d35503a634d11bf0474e4d85d1a47 schema:name doi
    79 schema:value 10.1007/s10114-018-7159-x
    80 rdf:type schema:PropertyValue
    81 anzsrc-for:03 schema:inDefinedTermSet anzsrc-for:
    82 schema:name Chemical Sciences
    83 rdf:type schema:DefinedTerm
    84 anzsrc-for:0306 schema:inDefinedTermSet anzsrc-for:
    85 schema:name Physical Chemistry (incl. Structural)
    86 rdf:type schema:DefinedTerm
    87 sg:journal.1040372 schema:issn 1439-7617
    88 1439-8516
    89 schema:name Acta Mathematica Sinica, English Series
    90 rdf:type schema:Periodical
    91 sg:person.015202174441.44 schema:affiliation https://www.grid.ac/institutes/grid.263761.7
    92 schema:familyName Qiu
    93 schema:givenName Jing Hui
    94 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015202174441.44
    95 rdf:type schema:Person
    96 sg:pub.10.1007/978-3-642-87561-8_12 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036656617
    97 https://doi.org/10.1007/978-3-642-87561-8_12
    98 rdf:type schema:CreativeWork
    99 sg:pub.10.1007/978-3-662-41914-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018897175
    100 https://doi.org/10.1007/978-3-662-41914-4
    101 rdf:type schema:CreativeWork
    102 sg:pub.10.1007/978-94-017-1588-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002266580
    103 https://doi.org/10.1007/978-94-017-1588-1
    104 rdf:type schema:CreativeWork
    105 sg:pub.10.1007/bf02192533 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015717068
    106 https://doi.org/10.1007/bf02192533
    107 rdf:type schema:CreativeWork
    108 sg:pub.10.1007/s00013-009-0072-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1043001860
    109 https://doi.org/10.1007/s00013-009-0072-x
    110 rdf:type schema:CreativeWork
    111 sg:pub.10.1007/s00186-006-0078-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041004172
    112 https://doi.org/10.1007/s00186-006-0078-0
    113 rdf:type schema:CreativeWork
    114 sg:pub.10.1007/s001860050032 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008319736
    115 https://doi.org/10.1007/s001860050032
    116 rdf:type schema:CreativeWork
    117 sg:pub.10.1007/s10107-008-0249-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001666377
    118 https://doi.org/10.1007/s10107-008-0249-2
    119 rdf:type schema:CreativeWork
    120 sg:pub.10.1007/s10114-011-0294-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003216092
    121 https://doi.org/10.1007/s10114-011-0294-2
    122 rdf:type schema:CreativeWork
    123 sg:pub.10.1007/s10114-013-2284-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1031156917
    124 https://doi.org/10.1007/s10114-013-2284-z
    125 rdf:type schema:CreativeWork
    126 sg:pub.10.1007/s10114-015-4541-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004601583
    127 https://doi.org/10.1007/s10114-015-4541-9
    128 rdf:type schema:CreativeWork
    129 sg:pub.10.1007/s10898-012-9983-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002364427
    130 https://doi.org/10.1007/s10898-012-9983-3
    131 rdf:type schema:CreativeWork
    132 sg:pub.10.1007/s10957-004-6472-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1003575664
    133 https://doi.org/10.1007/s10957-004-6472-y
    134 rdf:type schema:CreativeWork
    135 sg:pub.10.1023/a:1004619426652 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019934147
    136 https://doi.org/10.1023/a:1004619426652
    137 rdf:type schema:CreativeWork
    138 sg:pub.10.1023/b:jota.0000037602.13941.ed schema:sameAs https://app.dimensions.ai/details/publication/pub.1039210584
    139 https://doi.org/10.1023/b:jota.0000037602.13941.ed
    140 rdf:type schema:CreativeWork
    141 https://app.dimensions.ai/details/publication/pub.1002266580 schema:CreativeWork
    142 https://app.dimensions.ai/details/publication/pub.1018897175 schema:CreativeWork
    143 https://doi.org/10.1006/jmaa.2001.7709 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019888957
    144 rdf:type schema:CreativeWork
    145 https://doi.org/10.1016/0022-247x(74)90025-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024814013
    146 rdf:type schema:CreativeWork
    147 https://doi.org/10.1016/0362-546x(86)90126-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009491213
    148 rdf:type schema:CreativeWork
    149 https://doi.org/10.1016/j.jmaa.2008.04.055 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044182609
    150 rdf:type schema:CreativeWork
    151 https://doi.org/10.1016/j.jmaa.2008.06.020 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010217204
    152 rdf:type schema:CreativeWork
    153 https://doi.org/10.1016/j.jmaa.2010.09.014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050612852
    154 rdf:type schema:CreativeWork
    155 https://doi.org/10.1016/j.jmaa.2012.12.072 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023719776
    156 rdf:type schema:CreativeWork
    157 https://doi.org/10.1016/j.jmaa.2014.05.027 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003219716
    158 rdf:type schema:CreativeWork
    159 https://doi.org/10.1016/j.na.2005.04.011 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017093300
    160 rdf:type schema:CreativeWork
    161 https://doi.org/10.1016/j.na.2009.03.034 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009389647
    162 rdf:type schema:CreativeWork
    163 https://doi.org/10.1016/s0252-9602(12)60172-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036493151
    164 rdf:type schema:CreativeWork
    165 https://doi.org/10.1016/s0362-546x(02)00103-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029380498
    166 rdf:type schema:CreativeWork
    167 https://doi.org/10.1016/s0362-546x(98)00255-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008560415
    168 rdf:type schema:CreativeWork
    169 https://doi.org/10.1016/s0377-2217(02)00444-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044439244
    170 rdf:type schema:CreativeWork
    171 https://doi.org/10.1080/02331934.2010.522712 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007726467
    172 rdf:type schema:CreativeWork
    173 https://doi.org/10.1080/02331939208843815 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018896815
    174 rdf:type schema:CreativeWork
    175 https://doi.org/10.1090/s0002-9939-00-05717-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019577543
    176 rdf:type schema:CreativeWork
    177 https://doi.org/10.1090/s0002-9939-97-03864-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012166030
    178 rdf:type schema:CreativeWork
    179 https://doi.org/10.1090/s0273-0979-1979-14595-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003139392
    180 rdf:type schema:CreativeWork
    181 https://doi.org/10.1137/05062648x schema:sameAs https://app.dimensions.ai/details/publication/pub.1062846076
    182 rdf:type schema:CreativeWork
    183 https://doi.org/10.1137/060658989 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062849346
    184 rdf:type schema:CreativeWork
    185 https://doi.org/10.1137/060672868 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062849800
    186 rdf:type schema:CreativeWork
    187 https://doi.org/10.1137/090760660 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062856380
    188 rdf:type schema:CreativeWork
    189 https://doi.org/10.1137/110824115 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062864616
    190 rdf:type schema:CreativeWork
    191 https://doi.org/10.1142/5021 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098867970
    192 rdf:type schema:CreativeWork
    193 https://doi.org/10.4134/bkms.2002.39.4.535 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044547227
    194 rdf:type schema:CreativeWork
    195 https://www.grid.ac/institutes/grid.263761.7 schema:alternateName Soochow University
    196 schema:name School of Mathematical Sciences, Soochow University, 215006, Suzhou, P. R. China
    197 rdf:type schema:Organization
     




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


    ...