论文标题
通用 - hukuhara射门有效方向方法，用于解决间隔值函数及其在最小二乘问题中的优化问题
Generalized-Hukuhara-Gradient Efficient-Direction Method to Solve Optimization Problems with Interval-valued Functions and its Application in Least Squares Problems
论文作者
论文摘要
本文提出了一种通用的GH梯度效率方向方法和一种用于间隔值函数优化问题的W-GH梯度有效方法。提出了两种方法的收敛分析和逐步算法。可以观察到，W-GH梯度有效方法对于强凸间值的目标函数线性收敛。为了开发提出的方法并研究其收敛性，说明了强凸度的强烈概念和间隔值函数GH-持续性的顺序标准的概念。在续集中，还提出了对间隔值函数的GH差异性的新定义。借助新定义的线性间隔值函数概念来描述GH-差异性的新定义。注意到，提出的GH-差异性能力优于现有性。对于GH可分化的间隔值函数，得出了凸度与间隔值函数的GH级别的关系以及间隔优化问题的最佳条件。对于派生的最佳条件，引入了间隔值函数的有效方向概念。有效方向的想法用于开发提出的梯度方法。作为所提出方法的应用，通过W-GH梯度有效方法解决间隔值数据的最小平方问题。通过多项式拟合和逻辑曲线拟合来说明针对最小二乘问题的提出方法。
This article proposes a general gH-gradient efficient-direction method and a W-gH-gradient efficient method for the optimization problems with interval-valued functions. The convergence analysis and the step-wise algorithms of both the methods are presented. It is observed that the W-gH-gradient efficient method converges linearly for a strongly convex interval-valued objective function. To develop the proposed methods and to study their convergence, the idea of strong convexity and sequential criteria for gH-continuity of interval-valued function are illustrated. In the sequel, a new definition of gH-differentiability for interval-valued functions is also proposed. The new definition of gH-differentiability is described with the help of a newly defined concept of linear interval-valued function. It is noticed that the proposed gH-differentiability is superior to the existing ones. For a gH-differentiable interval-valued function, the relation of convexity with the gH-gradient of an interval-valued function and an optimality condition of an interval optimization problem are derived. For the derived optimality condition, a notion of efficient direction for interval-valued functions is introduced. The idea of efficient direction is used to develop the proposed gradient methods. As an application of the proposed methods, the least square problem for interval-valued data by W-gH-gradient efficient method is solved. The proposed method for least square problems is illustrated by a polynomial fitting and a logistic curve fitting.
