2022•应用数学和力学Open access
The Properties of Quasiconvex Functions and Their Applications in Multiobjective Optimization Problems
SHI Xiaobo, 重庆师范大学 数学科学学院，重庆 401331, GAO Ying
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Abstract
A new type of approximate subdifferential was proposed for quasiconvex functions. Their properties were studied, and the approximate subdifferential was applied to the characterization of approximate solutions to quasiconvex multiobjective optimization problems. Firstly, the existing approximate subdifferentials were improved to get a new approximate subdifferential of the quasiconvex function, and their relationships and properties were given. Then, the optimality conditions for approximate efficient solutions and approximate properly efficient solutions to quasiconvex multiobjective optimization problems were obtained by means of the new approximate subdifferential.