标题： 基于径向Epi导数的线搜索方法在非凸非光滑盒约束优化中的应用 显示英文标题

标题： Radial Epiderivative Based Line Search Methods in Nonconvex and Nonsmooth Box-Constrained Optimization

摘要： 本文提出了一种基于径向上导数的新型线搜索方法，用于求解非光滑且非凸的有界约束优化问题。采用径向上导数概念的理由在于它提供了识别全局下降方向以及实现非凸和不可微函数全局极小值的充分必要条件。这些径向上导数的特性与线搜索方法相结合，形成了迭代求解算法。所提出的算法在每次迭代中生成搜索方向，并通过径向上导数的能力执行全局下降方向和停止准则。我们使用两种线搜索方法，即循环坐标法和粒子群优化技术来生成仅表现出下降特性的搜索方向，这些下降特性由当前点处近似计算的径向上导数确定。作为特殊情况，这些方法被应用于凹函数的最小化问题。文中证明了两个收敛性定理，其中一个涉及一般的线搜索方法，仅涵盖该方法生成的方向集合；另一个收敛性定理则专门针对凹函数的最小化问题，不仅涵盖生成的方向集合，还涵盖了整个可行解集。所提出的方法性能通过文献中的经典基准问题进行了评估，结果显示了该方法在生成最优或接近最优解方面的优势。 显示英文摘要

摘要： In this paper, we develop a novel radial epiderivative-based line search methods for solving nonsmooth and nonconvex box-constrained optimization problems. The rationale for employing the concept of radial epiderivatives is that they provide necessary and sufficient conditions for both identifying global descent directions and achieving global minimum of nonconvex and nondifferentiable functions. These properties of radial epiderivatives are combined with line search methods to develop iterative solution algorithms. The proposed methods generate search directions at each iteration where global descent directions and stopping criteria are performed by using the abilities of the radial epiderivatives. We use two line search methods, that is cyclic coordinate and particle swarm optimization techniques to generate search directions, selecting only those that exhibit descent, as determined by using approximately computed radial epiderivatives at the current point. As a particular case, these methods are applied for minimizing concave functions. In the paper, two convergence theorems are proved. One of them deals with the general line search method and covers only the set of directions generated by the method. The second convergence theorem deals with minimizing concave functions which deals not only with the generated set of directions but covers the whole set of feasible solutions. The performance of the proposed method is evaluated by using well-known benchmark problems from the literature. The results demonstrate the advantages of the proposed approach in generating optimal or near-optimal solutions.