Some Notes on the Scalarization of Function Δ for Vector Optimization Problems

TANG Li-ping; LI Fei; ZHAO Ke-quan; YANG Xin-min

doi:10.3879/j.issn.1000-0887.2015.10.009

Volume 36 Issue 10

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TANG Li-ping, LI Fei, ZHAO Ke-quan, YANG Xin-min. Some Notes on the Scalarization of Function Δ for Vector Optimization Problems[J]. Applied Mathematics and Mechanics, 2015, 36(10): 1095-1106. doi: 10.3879/j.issn.1000-0887.2015.10.009

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Some Notes on the Scalarization of Function Δ for Vector Optimization Problems

doi: 10.3879/j.issn.1000-0887.2015.10.009

¹College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P.R.China;²School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China;³School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, P.R.China

Funds: The National Natural Science Foundation of China(Key Program)(11431004);The National Natural Science Foundation of China（General Program）(11271391;11201511;11301574)

Received Date: 2015-01-14
Rev Recd Date: 2015-08-13
Publish Date: 2015-10-15

Abstract

Abstract

Recently，Xia Yuan-mei,et al.(Journal of Chongqing Normal University(Natural Science), 2015,32(1): 12-15) studied the ?-properly efficient solutions to vector optimization problems via scalar function Δ in terms of the nonlinear scalarization method, and gave some examples to illustrate their results. It was point out here that theorem 1 established by Xia Yuan-mei,et al. was a special case of Theorem 4.6(i) obtained by Gao, et al.(Journal of Industrial and Management Optimization,2011,7（2）: 483-496), and the proof of Theorem 2 given by Xia Yuan-mei,et al. had some deficiency. Through investigation the nonlinear scalarization of function Δ for the (C, ε)-properly efficient solutions, theorem 2 obtained by Xia Yuan-mei, et al. was proved again rigorously. In the end, some examples in which ?-properly efficient solutions did exist, were given to illustrate the main results.
- vector optimization,
- approximate properly efficient solution,
- function Δ,
- nonlinear scalarization

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References(23)

References

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