Inexact Sequential Quadratic Optimization with Penalty Parameter Updates within the QP Solver
Inexact Sequential Quadratic Optimization with Penalty Parameter Updates within the QP Solver
复制标题
QP 求解器内带有惩罚参数更新的不精确序列二次优化
DOI：
10.1137/18m1176488
复制
发表时间：
2020
影响因子：
3.1
通讯作者：
Wang, Jiashan
中科院分区：
文献类型：
--
作者：
Burke, James V.;Curtis, Frank E.;Wang, Hao;Wang, Jiashan
本文重点研究了求解大规模非线性优化问题的顺序二次优化（通常称为SQP）方法。这种方法对计算量要求最高的方面是每次迭代期间搜索方向的计算，为此我们考虑使用无矩阵方法。特别地，我们开发了一种方法，该方法需要单个QP子问题的不精确解来建立整个SQP方法的收敛性。众所周知，SQP方法可能会受到全局收敛机制不良行为的困扰。为了解决这个问题，我们提出在子问题求解器中使用精确惩罚函数和动态惩罚参数更新策略，从而使结果搜索方向预测向可行性和最优性的进展。提出了参数更新策略，并证明在合理的假设下，该策略不会对惩罚参数进行不必要的修改。我们以数值实验结果的讨论来结束本文，这些结果说明了我们提出的技术的好处。
This paper focuses on the design of sequential quadratic optimization (commonly known as SQP) methods for solving large-scale nonlinear optimization problems. The most computationally demanding aspect of such an approach is the computation of the search direction during each iteration, for which we consider the use of matrix-free methods. In particular, we develop a method that requires an inexact solve of a single QP subproblem to establish the convergence of the overall SQP method. It is known that SQP methods can be plagued by poor behavior of the global convergence mechanism. To confront this issue, we propose the use of an exact penalty function with a dynamic penalty parameter updating strategy to be employedwithinthe subproblem solver in such a way that the resulting search direction predicts progress toward both feasibility and optimality. We present our parameter updating strategy and prove that, under reasonable assumptions, the strategy does not modify the penalty parameter unnecessarily. We close the paper with a discussion of the results of numerical experiments that illustrate the benefits of our proposed techniques.
求解约束非线性规划问题的鲁棒信赖域方法
影响因子：
3.1
作者：
J. Burke
通讯作者：
J. Burke
一种非线性优化的不精确序贯二次优化算法
影响因子：
3.1
作者：
Frank E. Curtis;T. C. Johnson;Daniel P. Robinson;A. Wächter
通讯作者：
A. Wächter