Power图是Voronoi图的扩展，具有精确容量限制、拓扑结构良好等特性，用途广泛。现有Power图计算算法或收敛速度慢，或不具有一般性，应用受到较大制约。课题聚焦于Power图计算问题：1）致力于提出一套统一的计算框架，来求解多约束Power图，包括容量约束、站点位置约束、站点拓扑约束、不同距离度量等及其组合，提高算法适用性和易用性；2）将其建模为多约束非线性优化问题，提出基于增广拉格朗日方法和拟牛顿法的算法方案，采用同时面向站点位置和权重的一体化优化策略，提升算法计算性能；3）在此基础上，提出定点Power图和变容量限制Power图这两种新变种和新问题，并给出求解方案；4）进一步引入GPU来加快Power图各费时计算环节，对离散域点交换法和连续域一体化优化算法二次加速，解决大规模站点时收敛慢问题。所提算法框架注重统一性、可扩展性和效率，力争成为Power图研究的一个重大进展。

Power diagram is the generalization of Voronoi diagram, and has characteristics of precise capacity constraint and good topological structures, thus is widely used in many domains. Existing power diagram generating algorithms suffer from the slow convergence speed, as well as the loss of generality. This proposal focuses on the research of power diagram computing method, and endeavor to present a uniform and all-in-one solving framework for multi-constraint power diagram, which can handle most applied cases including capacity restriction, site location constraint, site topology restrain, diverse distance definitions, and their arbitrary combinations. To solving the multi-constraint nonlinear optimization problem, this project proposes an augmented Lagrange method plus quasi-Newton based optimization schema and adopts synchronous strategy that optimizes the sites and weights at the same time, in order to comprehensively promote the usability for power diagram. Based on the above framework, the proposal firstly presents the problems and solving approaches for both fixed site centroidal capacity constrained power diagram and variable capacity constrained power diagram. Additionally, a GPU-assisted method is introduced to speed up the most expensive computing processes, and accelerate again the points-swapping approach in finite space and the proposed quasi-Newton method in continuous space, which aims to solve the problems with large-scale sites and complex density. The proposed approach focuses on algorithm unity, scalability and efficiency, and tries to edge itself as an important advance for the theoretical computation research of power diagram.