Complete scalarization of multi-objective optimization problems
Zhao Kequan, Yang Xinmin, Xia Yuanmei · Scientia Sinica Mathematica · 2019
In this paper, we first propose a kind of new scalarization optimization problem by using the slack variables and the extension of generalized Tchebycheff norm. Furthermore, we obtain some complete scalarization characterizations of weakly efficient solutions, efficient solutions and properly efficient solutions for a generalmulti-objective optimization problem by adjusting the ranges of several kinds of parameters. Moreover, we give an example to illustrate our main results, which verifies that whether a given feasible solution ofmulti-objective optimization problems is a weakly efficient solution, an efficient solution and a properly efficient solution by using the corresponding scalarization procedures.