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Recent Developments in Vector Optimization pp 467–515Cite as

Extended Pareto Optimality in Multiobjective Problems

Part of the Vector Optimization book series (VECTOROPT,volume 1)

Abstract

This chapter largely discusses some major notions of optimal/efficient solutions in multiobjective optimization and studies general necessary conditions for minimal points of sets and for minimizers of constrained set-valued optimization problems with respect to extended Pareto preference relations.

Keywords

  • Multiobjective Optimization
  • Minimal Point
  • Multiobjective Optimization Problem
  • Extremal Principle
  • Feasible Allocation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Acknowledgements

Research of the first author was partially supported by the NMU Faculty Grant FG-5-54844. Research of the second author was partially supported by the US National Science Foundation under grants DMS-0603846 and DMS-1007132 and by the Australian Research Council under grant DP-12092508.

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Authors and Affiliations

  1. Department of Mathematics & Computer Science, Northern Michigan University, Marquette, MI, 49855, USA

    Truong Q. Bao

  2. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    Boris S. Mordukhovich

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  1. Truong Q. Bao
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  2. Boris S. Mordukhovich
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Correspondence to Boris S. Mordukhovich .

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Editors and Affiliations

  1. Aligarh, 202001, Uttar Pradesh, India

    Qamrul Hasan Ansari

  2. , Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, 80424, Taiwan R.O.C.

    Jen-Chih Yao

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Bao, T.Q., Mordukhovich, B.S. (2012). Extended Pareto Optimality in Multiobjective Problems. In: Ansari, Q., Yao, JC. (eds) Recent Developments in Vector Optimization. Vector Optimization, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21114-0_13

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