Description

• Title:
  Necessary and Sufficient Conditions for Robust Minimal Solutions in Uncertain Vector Optimization
• Creator:
  Studniarski, Marcin;
  Stasiak, Aleksandra;
  Michalak, Anna
• Contributor:
  Faculty of Mathematics and Computer Science, University of Łódź, S. Banacha No. 22, 90-238, Łódź, Poland;
  Faculty of Economics and Sociology, University of Łódź, Rewolucji 1905 r. no. 41, 90-214, Łódź, Poland
• Description:
  Mathematics Subject Classification: 49J52, 49J53, 49N30, 90C31.;
  We introduce a new notion of a vector-based robust minimal solution for a vector-valued uncertain optimization problem, which is defined by means of some open cone. We present necessary and sufficient conditions for this kind of solution, which are stated in terms of some directional derivatives of vector-valued functions. To prove these results, we apply the methods of set-valued analysis. We also study relations between our definition and three other known optimality concepts. Finally, for the case of scalar optimization, we present two general algorithm models for computing vector-based robust minimal solutions.;
  The authors are grateful to the University of Łódź for providing necessary funds and conditions needed to complete this research.
• Object availability:
  free access
• Rights:
  Uznanie autorstwa 4.0 Międzynarodowe;
  http://creativecommons.org/licenses/by/4.0
• Date:
  2021.09.21;
  2020
• Type:
  Article
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Springer Nature
• Relation:
  Journal of Optimization Theory and Applications;186
• Subject:
  Uncertain optimization;
  Robust minimal solutions;
  Set-valued analysis;
  Radial derivatives
• Identifier:
  Studniarski, M., Michalak, A. & Stasiak, A. Necessary and Sufficient Conditions for Robust Minimal Solutions in Uncertain Vector Optimization. J Optim Theory Appl 186, 375–397 (2020). https://doi.org/10.1007/s10957-020-01714-w;
  0022-3239;
  http://hdl.handle.net/11089/39115 ;
  1573-2878;
  10.1007/s10957-020-01714-w
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  check license
• Type:
  image