论文标题
Moreau - dft中的Yosida正则化
Moreau--Yosida regularization in DFT
论文作者
论文摘要
Moreau-Yosida正规化被引入精确DFT的框架中。 Moreau-Yosida正规化是在可分离的希尔伯特空间上的较低半连续凸功能上进行的无损操作，当应用于精确DFT的通用功能（适当地限于有限域）时，对无效的$ V $ v $ v $ ablesentability问题进行了重新重新，并具有严格的严格且发散性且无限于Kohn Shym of shym ot shym shym of shym shym shym shym of shymy shym shym shym shym shym shym shym shym shym shym。 本章包括对精确DFT的独立介绍，凸出分析的基本工具，例如子和超差异性和凸结合，以及对Moreau-Yosida正则化的基本结果。然后将正则化应用于精确的DFT和Kohn-Sham理论，并分析基于最佳阻尼算法的基本迭代方案。特别是它的全球融合建立了。本章结束时提供了一些观点。
Moreau-Yosida regularization is introduced into the framework of exact DFT. Moreau-Yosida regularization is a lossless operation on lower semicontinuous proper convex functions over separable Hilbert spaces, and when applied to the universal functional of exact DFT (appropriately restricted to a bounded domain), gives a reformulation of the ubiquitous $v$-representability problem and a rigorous and illuminating derivation of Kohn-Sham theory. The chapter comprises a self-contained introduction to exact DFT, basic tools from convex analysis such as sub- and superdifferentiability and convex conjugation, as well as basic results on the Moreau-Yosida regularization. The regularization is then applied to exact DFT and Kohn-Sham theory, and a basic iteration scheme based in the Optimal Damping Algorithm is analyzed. In particular, its global convergence established. Some perspectives are offered near the end of the chapter.
