论文标题
非线性半决赛编程问题的稳定顺序二次半决赛方法的超线性和二次收敛
Superlinear and quadratic convergence of a stabilized sequential quadratic semidefinite programming method for nonlinear semidefinite programming problems
论文作者
论文摘要
在本文中，我们提出了一个稳定的非线性半趋势编程（NSDP）问题的稳定顺序二次半决赛（SQSDP）方法，并证明其局部收敛。稳定的SQSDP方法最初是为了解决退化的NSDP问题而开发的，并且基于非线性编程（NLP）问题的稳定顺序编程（SQP）方法。尽管已经提出了一些针对NSDP问题的SQP型方法，但其中大多数是基于NLP问题的SQP方法的SQSDP方法，关于稳定的SQSDP方法的研究很少。特别是，有开发局部快速收敛稳定的SQSDP方法的空间。我们不仅证明了高等教育，而且还证明了在某些温和的假设下所提出的方法的二次收敛，例如严格的鲁滨逊的约束资格和二阶足够条件。
In this paper, we present a stabilized sequential quadratic semidefinite programming (SQSDP) method for nonlinear semidefinite programming (NSDP) problems and prove its local convergence. The stabilized SQSDP method is originally developed to solve degenerate NSDP problems and is based on the stabilized sequential programming (SQP) methods for nonlinear programming (NLP) problems. Although some SQP-type methods for NSDP problems have been proposed, most of them are SQSDP methods which are based on the SQP methods for NLP problems, and there are few researches regarding the stabilized SQSDP methods. In particular, there is room for the development of locally fast convergent stabilized SQSDP methods. We prove not only superlinear but also quadratic convergence of the proposed method under some mild assumptions, such as strict Robinson's constraint qualification and second-order sufficient condition.
