论文标题
用于二次编程和低频升级的近端稳定内点方法，并更新了预处理技术
Proximal stabilized Interior Point Methods for quadratic programming and low-frequency-updates preconditioning techniques
论文作者
论文摘要
在这项工作中，在线性和二次编程的背景下，我们在近端方法的框架中解释了原始的双重正规化内部方法（PDR-IPMS）。关于收敛性和收敛速度的理论结果，最终稳定的IPM（PS-IPM）得到了强烈支持，并且可以处理退化问题。此外，在这项工作的第二部分中，我们分析了用于求解牛顿线性系统的线性代数例程的正则化参数与计算足迹之间的相互作用。特别是，当使用迭代的Krylov方法求解这些系统时，我们提出了通用预处理，该通用预定器利用正规化和SCHUR补体的新重新分组，对于随后的一系列IPM迭代而言仍然很有吸引力。因此，仅需要在总IPM迭代的一小部分中重新计算它们。允许使用预处理的低频更高的生成的正规化二阶方法，为第一和二阶方法之间的替代第三种方式铺平了路径。
In this work, in the context of Linear and Quadratic Programming, we interpret Primal Dual Regularized Interior Point Methods (PDR-IPMs) in the framework of the Proximal Point Method. The resulting Proximal Stabilized IPM (PS-IPM) is strongly supported by theoretical results concerning convergence and the rate of convergence, and can handle degenerate problems. Moreover, in the second part of this work, we analyse the interactions between the regularization parameters and the computational foot-print of the linear algebra routines used to solve the Newton linear systems. In particular, when these systems are solved using an iterative Krylov method, we propose general purpose preconditioners which, exploiting the regularization and a new rearrangement of the Schur complement, remain attractive for a series of subsequent IPM iterations. Therefore they need to be recomputed only in a fraction of the total IPM iterations. The resulting regularized second order methods, for which low-frequency-updates of the preconditioners are allowed, pave the path for an alternative third way in-between first and second order methods.
