Journal of the Operations Research Society of China ›› 2017, Vol. 5 ›› Issue (3): 419-430.doi: 10.1007/s40305-016-0139-x

Special Issue: Continuous Optimization

• Continuous Optimization • Previous Articles    

Conic Scalarizations for Approximate Efficient Solutions in Nonconvex Vector Optimization Problems

Hui Guo1 · Wan-li Zhang2   

  1. 1 Department of Mathematics, Chongqing Normal University, Chongqing 401331, China
    2 College of Electronic and Information Engineering, Southwest University, Chongqing 400715,China
  • Online:2017-09-30 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

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