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| 摘要: |
| 填充函数算法是求解全局优化问题的有效方法之一。在局部优化的方法中，梯度投影法因为简单实用而得到广泛的应用，而滤子作为评判标准以其良好的数值结果也成为求解问题的有效工具之一。为了优化全局优化的算法，本文将滤子技术和填充函数方法结合，提出一个基于梯度投影的广义填充函数滤子算法，用于求解带线性约束的非凸全局优化问题。文章首先给出一个新的广义填充函数并讨论了其相关性质，特别是该函数在边界上的表现。然后提出了任意初始点下求解约束全局优化问题的算法并证明了算法特性，尤其是边界问题的合理处理。最后列出的数值试验效果证明了算法的有效性。 |
| 关键词: 非凸全局优化 约束函数 填充函数 三维滤子 |
| DOI： |
| 分类号:O221.2 |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| A generalized filled function filter method based on gradient projection |
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Zhang Huiwen,Wang Wei
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| Abstract: |
| The filled function method is one of the effective methods established for solving global optimization problems. Among the methods for local optimization, the gradient projection method is widely used because of its simplicity and practicability. Due to excellent numerical results as evaluation criterion, the filter technique is regarded as one of the effective tools for optimization. In order to optimize the global optimization algorithm, this paper combines the filter technique with the filled function method, and presents a generalized filled function filter algorithm based on gradient projection for the non-convex global optimization problems with linear constraints. In this paper, a new generalized filled function is given and its characteristics are discussed, especially the performance on the boundary. Based on that the theoretical algorithm for global optimization with constraints with arbitrary initial points is proposed. And the properties and the reasonable disposal of boundary problems are proved. The numerical results are listed at last to show the effectiveness of the algorithm. |
| Key words: non-convex global optimization constraint function filled function three dimensional filter |
