函数强伪凸性与映射强伪单调性  

ON STRONG PSEUDOCONVEXITY AND STRONG PSEUDOMONOTONICITY

作　　者：杨益民[1] 

机构地区：[1]安徽机电学院运筹学研究室,芜湖241000

出　　处：《高等学校计算数学学报》2000年第2期141-146,共6页Numerical Mathematics A Journal of Chinese Universities

基　　金：安徽省高校中青年学科带头人培养基金资助

摘　　要：New concepts of strongly pseudoconvex functions and strongly pseudomonotone maps are introduced, which are stronger than corresponding concepts in ref.2. It is shown that strong pseudomonotonicity of the gradient corresponds to strong pseudoconvexity of the underlying function, without any other assumption of the function. Point out the error example 3.1 in ref.2, and give a right counterexample. Also, for an open question in ref.1, a very simple counterexample is presented.New concepts of strongly pseudoconvex functions and strongly pseudomonotone maps are introduced, which are stronger than corresponding concepts in ref.2. It is shown that strong pseudomonotonicity of the gradient corresponds to strong pseudoconvexity of the underlying function, without any other assumption of the function. Point out the error example 3.1 in ref.2, and give a right counterexample. Also, for an open question in ref.1, a very simple counterexample is presented.

关 键 词：函数 强伪凸性 映射 强伪单调性 

分 类 号：O224[理学—运筹学与控制论] O174.13[理学—数学]