Fast Algorithms for Large Scale Convex Optimization Involving Linear Matrix Inequality

涉及线性矩阵不等式的大规模凸优化的快速算法

• 批准号: 9411664
• 负责人: Ko-Hui Michael Fan
• 金额: $ 16.32万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-09-15 至 1998-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9411664&HistoricalAwards=false
• 关键词: Fast; Algorithms; Large; Scale; Convex

9411664 Fan With recent dramatic increase in available computing power, numerical optimization has become an attractive tool for analysis and design of complex systems. There are a large number of problems in science and engineering which can be formulated as convex optimization problems involving linear matrix inequality. This problem is inherently difficult to solve as the nonsmoothness usually occurs at the solution. Further, as systems are becoming more complex, the resulting optimization problems tend to have a large number of decision variables as well as constraints. Therefore, several basic computation components such as inversion of a matrix, eigenvalue and eigenvector calculation, or evaluation of the Hessian matrix, that needed for most methods become either prohibited or very costly to perform. It is then necessary to use approximations and yet have the fast rate of convergence preserved. ***

随着近年来计算能力的急剧提高，数值优化已经成为复杂系统分析和设计的一个有吸引力的工具。 在科学和工程中有大量的问题可以转化为涉及线性矩阵不等式的凸优化问题。 这个问题本身就很难解决，因为非光滑性通常发生在解处。 此外，随着系统变得越来越复杂，所产生的优化问题往往具有大量的决策变量以及约束。 因此，大多数方法所需的几个基本计算组件，例如矩阵求逆、特征值和特征向量计算或Hessian矩阵的评估，变得被禁止或执行起来非常昂贵。 然后，有必要使用近似，但仍保持快速收敛。 ***