Analysis of inexact trust-region SQP algorithms
Analysis of inexact trust-region SQP algorithms
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DOI：
10.1137/s1052623499361543
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发表时间：
2001-01-04
影响因子：
3.1
通讯作者：
Vicente, LN
中科院分区：
文献类型：
--
作者：
Heinkenschloss, M;Vicente, LN
在本文中，我们推广了一类复合步长信赖域二次规划方法的设计及其全局收敛分析，以允许不精确的问题信息。不精确的问题信息可以由信赖域SQP方法中的迭代线性系统求解或一阶导数的近似产生。我们的信赖域SQP方法的精度要求是根据迭代的可行性和最优性进行调整的。我们的精度要求是笼统的，但我们展示了如何使用SQP方法的无矩阵实现中已有的信息来强制执行这些要求。在没有不精确的情况下，我们的全局收敛理论等同于Dennis，El-Alem和Maciel的理论[SIAM J.Optim.，7(1997)，pp.177-207]。如果所有的迭代都是可行的，即如果所有的迭代都满足等式约束，则我们的结果与无约束优化问题的具有不精确梯度信息的信赖域方法的已知收敛分析有关。
In this paper we extend the design of a class of composite-step trust-region SQP methods and their global convergence analysis to allow inexact problem information. The inexact problem information can result from iterative linear system solves within the trust-region SQP method or from approximations of first-order derivatives. Accuracy requirements in our trust-region SQP methods are adjusted based on feasibility and optimality of the iterates. Our accuracy requirements are stated in general terms, but we show how they can be enforced using information that is already available in matrix-free implementations of SQP methods. In the absence of inexactness our global convergence theory is equal to that of Dennis, El-Alem, and Maciel [SIAM J. Optim., 7 (1997), pp. 177-207]. If all iterates are feasible, i.e., if all iterates satisfy the equality constraints, then our results are related to the known convergence analyses for trust-region methods with inexact gradient information for unconstrained optimization.