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Boundedness and Nonemptiness of the Efficient Solution Sets in Multiobjective Optimization

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Abstract

For a given multiobjective optimization problem, we study recession properties of the sets of efficient solutions and properly efficient solutions. We work out various consequences based on the obtained recession properties, including a characterization for the boundedness and nonemptiness of the set of (properly) efficient solutions when the problem is a convex problem. We also show that the boundedness and nonemptiness of the set of efficient solutions is equivalent to that of the set of properly efficient solutions under an additional mild condition. Finally, we provide some new verifiable necessary conditions for the nonemptiness of the set of efficient solutions in terms of the associated recession functions and recession cones.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois, USA

    S. Deng

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  1. S. Deng
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Correspondence to S. Deng.

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Communicated by X.Q. Yang.

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Deng, S. Boundedness and Nonemptiness of the Efficient Solution Sets in Multiobjective Optimization. J Optim Theory Appl 144, 29–42 (2010). https://doi.org/10.1007/s10957-009-9589-1

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  • DOI: https://doi.org/10.1007/s10957-009-9589-1

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