论文标题
正规化的内点方法，用于约束优化和控制
Regularized Interior Point Methods for Constrained Optimization and Control
论文作者
论文摘要
鉴于控制应用程序，正规化和内部方法提供了有价值的观点，可以解决受约束的非线性优化问题。本文讨论了这些技术之间的相互作用，并提出了一种协同结合它们的算法。构建一系列密切相关的子问题并大致解决了每个问题，这种方法本质上利用了温暖的启动，提前终止，并且可能采用针对特定问题结构量身定制的亚种。此外，通过放宽近端惩罚的平等约束，正规化的子问题是可行的，可以通过构造来满足强大的约束资格，从而可以安全地利用有效的求解器。我们展示了正则化如何使潜在的线性代数和详细的收敛分析受益，这表明限制点倾向于最大程度地减少约束违规并满足适当的最佳条件。最后，我们在鲁棒性方面报告了数值结果，这表明合并的方法与内部点和增强的拉格朗日代码进行了比较。
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an algorithm that synergistically combines them. Building a sequence of closely related subproblems and approximately solving each of them, this approach inherently exploits warm-starting, early termination, and the possibility to adopt subsolvers tailored to specific problem structures. Moreover, by relaxing the equality constraints with a proximal penalty, the regularized subproblems are feasible and satisfy a strong constraint qualification by construction, allowing the safe use of efficient solvers. We show how regularization benefits the underlying linear algebra and a detailed convergence analysis indicates that limit points tend to minimize constraint violation and satisfy suitable optimality conditions. Finally, we report on numerical results in terms of robustness, indicating that the combined approach compares favorably against both interior point and augmented Lagrangian codes.
