论文标题
间隔值功能的广义Hukuhara Hadamard衍生物及其在间隔优化的应用
Generalized Hukuhara Hadamard Derivative of Interval-valued Functions and Its Applications to Interval Optimization
论文作者
论文摘要
在本文中，我们研究了间隔值函数（IVFS）的GH-HADAMARD衍生物的概念及其在间隔优化问题（IOPS）中的应用。结果表明，GH-HADAMARD衍生物的存在意味着GH-Frechet衍生物的存在，反之亦然。此外，证明GH-HADAMARD衍生物的存在意味着IVF的GH-持续性的存在。我们发现，Hadamard可区分的实值函数和GH-HADAMARD可区分的IVF的组成是GHADAMARD可区分的。此外，对于有限的可比IVF，我们证明所有有限可比IVF的最大值的GH-HADAMARD衍生物是其GH-HADAMARD衍生物的最大值。观察到所提出的衍生物对于检查IVF的凸度并表征IVF优化问题的有效点很有用。对于凸IVF，我们证明，如果在某个点GH-HADAMARD衍生物不占主导地位，则该点是一个有效的点。此外，事实证明，在有效的点上，GH-HADAMARD衍生物不主导零，也包含零。对于约束IOPS，我们通过使用拟议的导数证明了扩展的Karush-Kuhn-Tucker条件。整个研究得到了合适的例子的支持。
In this article, we study the notion of gH-Hadamard derivative for interval-valued functions (IVFs) and its applications to interval optimization problems (IOPs). It is shown that the existence of gH-Hadamard derivative implies the existence of gH-Frechet derivative and vise-versa. Further, it is proved that the existence of gH-Hadamard derivative implies the existence of gH-continuity of IVFs. We found that the composition of a Hadamard differentiable real-valued function and a gH-Hadamard differentiable IVF is gHHadamard differentiable. Further, for finite comparable IVF, we prove that the gH-Hadamard derivative of the maximum of all finite comparable IVFs is the maximum of their gH-Hadamard derivative. The proposed derivative is observed to be useful to check the convexity of an IVF and to characterize efficient points of an optimization problem with IVF. For a convex IVF, we prove that if at a point the gH-Hadamard derivative does not dominate to zero, then the point is an efficient point. Further, it is proved that at an efficient point, the gH-Hadamard derivative does not dominate zero and also contains zero. For constraint IOPs, we prove an extended Karush-Kuhn-Tucker condition by using the proposed derivative. The entire study is supported by suitable examples.
