数学
凸性
一般化
集合函数
最优化问题
集合(抽象数据类型)
非线性系统
数学优化
对偶(序理论)
应用数学
功能(生物学)
离散数学
数学分析
计算机科学
金融经济学
物理
生物
进化生物学
量子力学
经济
程序设计语言
作者
Elvira Hernández,Luis Rodríguez-Marín
标识
DOI:10.1016/j.jmaa.2006.01.033
摘要
The aim of this work is to obtain scalar representations of set-valued optimization problems without any convexity assumption. Using a criterion of solution introduced by Kuroiwa [D. Kuroiwa, Some duality theorems of set-valued optimization with natural criteria, in: Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis, World Scientific, River Edge, NJ, 1999, pp. 221–228], which is based on ordered relations between sets, we characterize this type of solutions by means of nonlinear scalarization. The scalarizing function is a generalization of the Gerstewitz's nonconvex separation function. As applications of our results we give two existence theorems for set-valued optimization problems.
科研通智能强力驱动
Strongly Powered by AbleSci AI