Permanently Going Back and Forth between the ``Quadratic World'' and the ``Convexity World'' in Optimization
Permanently Going Back and Forth between the ``Quadratic World'' and the ``Convexity World'' in Optimization
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DOI：
10.1007/s00245-001-0034-6
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发表时间：
2002
影响因子：
1.8
通讯作者：
J. Hiriart-Urruty;M. Torki
中科院分区：
文献类型：
--
作者：
J. Hiriart-Urruty;M. Torki
这项工作有两个目标。首先，我们提出了一个审查不同的结果，关于凸性的图像的二次映射，把他们在一个时间顺序的角度来看。接下来，我们启发这些结果从几何的角度来看，以提供新的和全面的证明，并沉浸在一个更一般和抽象的背景下。关键词：二次函数，值域凸性，联合正定性\amsclass{90C20，52A20，15A60.}
The objective of this work is twofold. Firstly, we propose a review of different results concerning convexity of images by quadratic mappings, putting them in a chronological perspective. Next, we enlighten these results from a geometrical point of view in order to provide new and comprehensive proofs and to immerse them in a more general and abstract context. \keywords{Quadratic functions, Range convexity, Joint positive definiteness.} \amsclass{90C20, 52A20, 15A60.}