The theory of increasing and convex-along-rays (ICAR) functions defined on a convex cone in a real locally convex topological vector space X was already well developed. In this paper, we first examine abstract convexity of increasing plus-convex-along-rays (IPCAR) functions defined on a real normed linear space X. We also study, for this class of functions, some concepts of abstract convexity, such as support sets and subdifferentials. Finally, as an application, we characterize the maximal elements of the support set of strictly IPCAR functions and give optimality conditions for the global minimum of the difference between two IPCAR functions.

中文翻译：

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两个递增的正凸沿射线函数之差的全局优化

定义在实局部凸拓扑向量空间 X 中的凸锥上的递增和凸沿射线 (ICAR) 函数理论已经得到很好的发展。在本文中，我们首先研究了定义在实范数线性空间 X 上的递增正凸沿射线 (IPCAR) 函数的抽象凸性。我们还研究了此类函数的一些抽象凸性概念，例如支持集和次微分。最后，作为一个应用，我们刻画了严格 IPCAR 函数支持集的最大元素，并给出了两个 IPCAR 函数之间差异的全局最小值的最优条件。