Large-Scale Constrained Optimization

这个项目的目标是发展有效的数值方法 用于解决复杂的非线性优化问题。 的 要开发和分析的算法遵循两个不同的，但 相关办法： - 序列二次规划（SQP）方法; - 屏障方法（即内部方法）。 这项研究将集中在大规模的问题，直接 稀疏线性和非线性约束的处理，以及 保证超线性收敛。 SQP方法的研究将扩展基于 线性约束子问题和一个增广拉格朗日价值 功能 要考虑的问题包括使用减少的 Hessian，精确二阶导数的使用，接受策略 子问题的不精确解，以及处理 不可行子问题 屏障法的工作已经证明非常成功 线性规划。 许多研究仍有待改进， 可靠性，并将其应用扩展到大规模 非线性（和凸）问题。 屏障法研究 强调矩阵分解而不是矩阵更新， 可以利用大量关于因子分解的研究， 并行和向量架构的机器的方法。 我们 提出直接和迭代方法来解决 不确定的系统。

The goal of this project is to develop effective numerical methods for solving complex nonlinear optimization problems. The algorithms to be developed and analyzed follow two distinct but related approaches: - Sequential quadratic programming (SQP) methods; and - Barrier methods (i.e. interior methods). This research will concentrate on large-scale problems, direct treatment of sparse linear and nonlinear constraints, and the guarantee of superlinear convergence. The research on SQP methods will extend techniques based on linearly constrained subproblems and an augmented Lagrangian merit function. Topics to be considered include use of a reduced Hessian, use of exact second derivatives, strategies for accepting inexact solutions of subproblems, and techniques for treating infeasible subproblems. Work in barrier methods have already proved remarkably successful for linear programs. Much research remains to improve their reliability and to extend their application to large-scale nonlinear (and convex) problems. Research in barrier methods emphasizes matrix factorization rather than matrix updating, and can utilize the substantial body of research on factorization methods for machines with parallel and vector architectures. We propose both direct and iterative methods for solving the indefinite systems involved.