New Methods for Nonlinear Optimization

非线性优化的新方法

• 批准号: 8702403
• 负责人: Richard Byrd
• 金额: $ 21.18万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-08-01 至 1990-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8702403&HistoricalAwards=false
• 关键词: New; Methods; Nonlinear; Optimization

Professors Byrd and Schnabel will continue their research in unconstrained and constrained optimization. Four topics are investigated. First, tensor methods for unconstrained optimization and initial development of such methods for constrained optimization. Second, trust region methods for constrained optimization that are relatively easy to implement, have satisfactory local and global convergence theory even in the presence of linearly dependent constraint gradients and perform efficiently and robustly in practice. Third, the development of algorithms for solving implicit least squares problems, a version of least squares that arises in curve fitting or where there are no dependent variables. Fourth, a thorough analysis of several quasi-Newton methods for nonlinearly constrained optimization, with the goal of guaranteeing local superlinear convergence with an arbitrary positive definite initial Hessian approximation, extending Powell's results for the BFGS methods. This research addresses important optimization problems that occur in many applications.

伯德和施纳贝尔教授将继续他们的研究， 无约束和约束优化。 四个主题是 研究了 首先，张量方法无约束优化和 这种方法的约束优化的初步发展。 第二，约束优化的信赖域方法， 相对容易实施，具有令人满意的本地和全球 收敛理论，即使存在线性相关 约束梯度，并在实践中有效和鲁棒地执行。 第三，发展求解隐式最小二乘的算法 问题，在曲线拟合中出现的最小二乘版本，或 这里没有因变量。 第四，深入分析 非线性约束优化的几种拟牛顿法， 目标是保证局部超线性收敛， 任意正定初始Hessian逼近，推广 Powell的BFGS方法结果。 这项研究解决了重要的优化问题， 许多应用程序。