论文标题
在非convex优化中的径向增长功能和规律性条件上
On radially epidifferentiable functions and regularity conditions in nonconvex optimization
论文作者
论文摘要
在本文中，我们研究了非凸函数的径向流动性概念，该函数扩展了（经典）定向派生概念。该论文介绍了这个概念的新定义和新属性，并建立了径向流离失所，克拉克的定向衍生物，岩石费尔的下降和定向衍生物之间的关系。径向流动性概念用于在没有凸条件的情况下建立新的规律条件。本文通过本文中研究的广义衍生物进行了非凸优化的全球最佳优化的必要条件。我们为下降方向建立了必要且充分的条件，以实现径向增长的非凸功能。该论文介绍了根据径向表现因素计算弱亚级别的明确配方，反之亦然，从开发解决方案方法的角度来看，这是在寻找非平滑和非凸优化的全局最佳选择的角度。本文中介绍的所有属性和定理都在示例中进行了说明和解释。
In this paper we study the radial epiderivative notion for nonconvex functions, which extends the (classical) directional derivative concept. The paper presents new definition and new properties for this notion and establishes relationships between the radial epiderivative, the Clarke's directional derivative, the Rockafellar's subderivative and the directional derivative. The radial epiderivative notion is used to establish new regularity conditions without convexity conditions. The paper analyzes necessary and sufficient conditions for global optimums in nonconvex optimization via the generalized derivatives studied in this paper. We establish a necessary and sufficient condition for a descent direction for radially epidifferentiable nonconvex functions. The paper presents explicit formulations for computing the weak subgradients in terms of the radial epiderivatives and vice versa, which are very important from point of view of developing solution methods for finding global optimums in nonsmooth and nonconvex optimization. All the properties and theorems presented in this paper, are illustrated and interpreted on examples.
