The Adaptive Parameter Control Method and Linear Vector Optimization
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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.
KeywordsVector 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
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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