On Marginal Subgradients of Convex Functions

摘要：

For a lower semicontinuous and proper convex function f with nonempty minimizer set and a point x in its domain, a marginal subgradient of f at x is a vector in df(x) with the smallest norm. We denote the norm of the marginal subgradient of f at x by g(x), it is known that the infimum of g(x) over a level set of f is nondecreasing from a lower level set to a higher level set. In this paper we study another aspect of the marginal subgradients, namely the monotonicity of the infimum of g(x) over an equidistance contour from the minimizer set. The results are applied to the study of some growth properties of the marginal subgradients.

作者: Roxin Zhang

作者单位: Department of Mathematics and Computer Science Northern Michigan University Marquette,Ml 49855,USA

会议类型: 国际会议

会议名称: The Third International Joint Conference on Computational Science and Optimization(第三届计算科学与优化国际大会 CSO 2010)

会议地点: 黄山

会议语种:英文

页码: 90-93

在线出版日期: 2010-05-28（万方平台首次上网日期，不代表论文的发表时间）