• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Construction of multiobjective optimization theory based on new definitions of supremum and infimum in the multi-dimensional extended real space

Research Project

Project/Area Number 14550400
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field System engineering
Research InstitutionOsaka University

Principal Investigator

TANINO Tetsuzo  Osaka University Graduate School of Engineering, Professor, 大学院・工学研究科, 教授 (50125605)

Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2003: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2002: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywordsmultiobjective optimization / supremum / infimum / convexity / stability / sensitivity analysis / conjugate mapping / duality
Research Abstract

In this paper, solutions for a multiobjective optimization problem are defined as the infimum of a set in the multi-dimensional extended real space and mathematical theory of multiobjective optimization is constructed.
First, we provided new definitions of supremum and infimum of a set in the extended real space, and investigated their properties. Particularly, taking infimum is regarded as an operator and some relationships between this operator and set theoretic operations such as the union and the algebraic sum are made clear. We introduced dividing and traversing properties of sets in the extended real space and proved that the infimum of an arbitrary set has these properties. This enabled us to characterize optimal solutions for a multiobjective optimization problem, particularly in the convex case.
Secondly, concepts of conjugate mappings and subgradients for set-valued mappings in the extended real space were introduced and conjugate duality theory was developed based on those concepts. A relationship between subgradients and conjugate mappings was provided and sufficient conditions for subdifferentiability of set-valued mappings were studied. A primal multiobjective optimization problem was imbedded into a family of perturbed problems and its dual problem was defined in terms of the conjugate mapping. Some duality results were established between the primal problem and the dual problem.
Furthermore, the perturbation mapping was defined for a parameterized multiobjective optimization problem, and its behavior was analyzed. From a qualitative viewpoint, continuity of the perturbation mapping was considered. On the other hand, from a quantitative viewpoint, graphical derivatives of the perturbation mapping were studied.
The obtained results contribute to construct a new theory of multiobjective optimization.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (9 results)

All Other

All Publications (9 results)

  • [Publications] Tetsuzo Tanino: "Multiobjective conjugate duality in the multi-dimensional extended real space"Proceedings of 2nd International Conference on Nonlinear Analysis and Convex Analysis. 489-499 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tetsuzo Tanino: "Some fundamental results for the infimum of a set in the multi-dimensional extended real space"Journal of Nonlinear and Convex Analysis. 5(in press). (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tetsuzo Tanino: "Multiobjective conjugate duality in the multi-dimensional extended real space"Proceedings of 2nd International Conference on Nonlinear Analysis and Convex Analysis. 489-499 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tetsuzo Tanino: "Some fundamental results for the infimum of a set in the multi-dimensional extended real space"Journal of Nonlinear and Convex Analysis. Vol.5 (in press). (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Tetsuzo Tanino: "Multiobjective conjugate duality in the multi-dimensional extended real space"Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis 2001. 489-499 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Tetsuzo Tanino: "Some fundamental results for the infimum of a set in the multi-dimensional extended real space"Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis 2003. (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Tetsuzo Tanino: "Theory of multiobjective optimization in the multi-dimensional extended real space"The 6^<th> International Multi-Objective Programming and Goal Programming Conference. (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Tetsuzo Tanino: "Multiobjective conjugate duality in the multi-dimensional extended real space"Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis 2001. 489-499 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Tetsuzo Tanino: "Multiobjective optimization based on a new definition of infimum"Proceedings of the First Korea-Japan Joint Symposium on Nonlinear Functional Analysis and Convex Analysis. (2003)

    • Related Report
      2002 Annual Research Report

URL: 

Published: 2002-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi