SIAM Journal on Optimization, Volume 31, Issue 3, Page 1774-1796, January 2021.
Various characterizations of convexity for images of a vector mapping where some of its components are quadratic and the remaining ones are linear are established. In a certain sense, one might conclude that convexity of the full image is reduced to the convexity of an image in a lower dimension by deleting the linear components. The latter may be considered as the analogue to the reduction of the number of constraints once the dual is associated. The cases of having one or two quadratic components while the other are linear are particularly analyzed. This allows us to formulate some (geometric) sufficient and necessary conditions for convexity. As a byproduct, a result obtained in [Xia, Wang, and Sheu, Math. Program. Ser. A, 156 (2016), pp. 513--547] is corrected. Finally, as some applications, we obtain an S-lemma (with equality and on an affine subspace) and a characterization of strong duality in terms of convexity of some image set associated to the minimization problem under consideration.

中文翻译：

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在非凸二次优化中应用二次线性映射来表征图像的凸性

SIAM 优化杂志，第 31 卷，第 3 期，第 1774-1796 页，2021 年 1 月。
建立了向量映射图像的凸性的各种特征，其中一些分量是二次的，其余的是线性的。在某种意义上，人们可能会得出结论，通过删除线性分量，可以将整个图像的凸度降低为图像在较低维度上的凸度。后者可以被认为是与对偶关联后减少约束数量的类似物。特别分析了具有一个或两个二次分量而另一个是线性的情况。这使我们能够为凸性制定一些（几何）充分和必要条件。作为副产品，在 [Xia, Wang, and Sheu, Math. 程序。爵士。A, 156 (2016), pp. 513--547] 已更正。最后，作为一些应用程序，