Vietnam Journal of Mathematics

, Volume 43, Issue 2, pp 471–486 | Cite as

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.

Keywords

Vector optimization Linear vector optimization Pascoletti–Serafini’s scalarization method Eichfelder’s adaptive parameter control method Sensitivity analysis in linear programming 

Mathematics Subject Classification (2010)

90C29 90C31 90C05 
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Notes

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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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Department of Information TechnologyLe Qui Don UniversityHanoiVietnam
  2. 2.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam

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