Journal of the Operations Research Society of China >

2017 , Vol. 5 >Issue 3: 419 - 430

DOI: https://doi.org/10.1007/s40305-016-0139-x

Continuous Optimization

Conic Scalarizations for Approximate Efficient Solutions in Nonconvex Vector Optimization Problems

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  • 1 Department of Mathematics, Chongqing Normal University, Chongqing 401331, China
    2 College of Electronic and Information Engineering, Southwest University, Chongqing 400715,China

Online published: 2017-09-30

Supported by

This research was supported by the National Natural Science Foundation of China (No. 11301574),Chongqing Municipal Education Commission (No. KJ1500310), and the Doctor Startup Fund of Chongqing Normal University (No.16XLB010).

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Abstract

Nonlinear scalarization is a very important method to deal with the vector optimization problems. In this paper, some conic nonlinear scalarization characterizations
of E-optimal points, weakly E-optimal points, and E-Benson properly efficient points proposed via improvement sets are established by a new scalarization function,
respectively. These results improved and generalized some previously known results.As a special case, the scalarization of Benson properly efficient points is also given. Some examples are given to illustrate the main results.

Key words： Improvement set ·; E-optimal points ·; Weakly E-optimal points ·E-Benson properly efficient points ·; Nonlinear scalarization

Cite this article

Hui Guo · Wan-li Zhang . Conic Scalarizations for Approximate Efficient Solutions in Nonconvex Vector Optimization Problems[J]. Journal of the Operations Research Society of China, 2017 , 5(3) : 419 -430 . DOI: 10.1007/s40305-016-0139-x

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