Projected Hessian Updating Methods

投影 Hessian 更新方法

• 批准号: 8713893
• 负责人: Chaya Gurwitz
• 金额: $ 11.76万
• 依托单位: CUNY Brooklyn College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-02-15 至 1991-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8713893&HistoricalAwards=false
• 关键词: Projected; Hessian; Updating; Methods

This project will investigate numerical methods for solving nonlinear programming problems. The problems involve minimizing a nonlinear function subject to a set of nonlinear equality and inequality constraints. Sequential quadratic programming (SQP) methods are particularly effective for solving problems of this nature. It is assumed that first derivatives of the objective and constraint functions are available, but that second derivatives may be too expensive to compute. Instead the methods typically update a suitable matrix which approximates second derivative information each iteration. We are interested in developing SQP methods which maintain an approximation to second derivative information projected onto the tangent space of the constraints. The main motivation for the work is that only the projected matrix enters into the optimality conditions for the nonlinear problem. We will investigate issues relating to both the global and local convergence properties of algorithms. These include the choice of quasi-Newton update, active set strategy and merit function. The main goal is two-fold: to produce efficient and reliable software and to provide a theoretical framework for these methods.

本项目将研究解决非线性问题的数值方法 编程问题。 问题涉及最小化非线性 服从一组非线性等式和不等式的函数 约束 序列二次规划（SQP）方法 对于解决这种性质的问题特别有效。 是 假设目标和约束的一阶导数 函数是可用的，但二阶导数也可能是可用的。 昂贵的计算。 相反，这些方法通常会更新合适的 每个迭代近似二阶导数信息的矩阵。 我们有兴趣开发SQP方法， 近似的二阶导数信息投影到 约束的切线空间。 这项工作的主要动机是 只有投影矩阵进入最优性条件 对于非线性问题。 我们将调查与这两方面有关的问题。 算法的全局和局部收敛性。 这些 包括拟牛顿更新的选择、有效集策略和 优值函数 主要目标是 双重：生产高效可靠的软件，并提供 这些方法的理论框架。