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The Adaptive Parameter Control Method and Linear Vector Optimization

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Abstract

The question of constructing a set of equidistant points, with a given small approximate distance, in the efficient and weakly efficient frontiers of a linear vector optimization problem of a general form, is considered in this paper. It is shown that the question can be solved by combining Pascoletti–Serafini’s scalarization method (1984) and Eichfelder’s adaptive parameter control method (2009) with a sensitivity analysis formula in linear programming, which was obtained by J. Gauvin (2001). Our investigation shows that one can avoid the strong second-order sufficient condition used by G. Eichfelder, which cannot be imposed on linear vector optimization problems.

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Acknowledgments

The research of N. T. T. Huong is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2014.39 and supported in part by Department of Information Technology, Le Qui Don University. The research of N. D. Yen is funded by the Vietnam Institute for Advanced Study in Mathematics (VIASM) and supported in part by Institute of Mathematics, Vietnam Academy of Science and Technology. The authors would like to thank the two anonymous referees for their very careful reading and helpful suggestions.

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Authors and Affiliations

  1. Department of Information Technology, Le Qui Don University, 236 Hoang Quoc Viet, Hanoi, Vietnam

    Nguyen Thi Thu Huong

  2. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, 10307, Vietnam

    Nguyen Dong Yen

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  1. Nguyen Thi Thu Huong
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  2. Nguyen Dong Yen
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Correspondence to Nguyen Dong Yen.

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Dedicated to Professor Nguyen Khoa Son on the occasion of his sixty-fifth birthday.

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Thu Huong, N.T., Yen, N.D. The Adaptive Parameter Control Method and Linear Vector Optimization. Vietnam J. Math. 43, 471–486 (2015). https://doi.org/10.1007/s10013-015-0144-0

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  • DOI: https://doi.org/10.1007/s10013-015-0144-0

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