• 主题
高级搜索  >
历史搜索 清空历史
首页> 美国政府科技报告 >Quasi-Convex and Pseudo-Convex Functions on Solid Convex Sets.
【24h】

Quasi-Convex and Pseudo-Convex Functions on Solid Convex Sets.

机译：实凸集上的拟凸和伪凸函数。

获取原文
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

The purpose of the paper is to prove that testing quasi-convexity (pseudo-convexity) of quadratic functions on solid convex sets can be reduced to an examination of finitely many conditions. One determines two maximal domains of quasi-convexity (pseudo-convexity) for the quadratic form Psi(x) = (x,Dx) where D has exactly one negative eigenvalue,and conversely,one shows that if the quadratic form Psi is quasi-convex (pseudo-convex) on a solid convex set,then the matrix D has exactly one negative eignevalue and the solid convex set is contained in one of the maximal domains. The special case when the solid convex set is the nonnegative (semi-positive) orthant is also analyzed. This study is then extended to quadratic functions Phi(x) = 1/2(x,Dx) + (c,x). Analogous results hold under the additional condition that the set (a/Da+c = 0) is not empty. In the last part of this paper,one analyzes functions that are not necessarily quadratic. One obtains some results on mathematical programming problems having twice differentiable quasi-convex objective function and constraint functions. Finally,one gives a necessary condition and a sufficient condition for the quasi-convexity of a function in Class C squared (i.e.,twice continuously differentiable) on a solid convex set. One also establishes a relation between the quasi-convexity and the pseudo-convexity of twice differentiable functions on solid convex sets. (Author)

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号