报告主题：Quadratic convergence to the optimal solution of second order conic optimization
报告人：Tamás Terlaky 教授 （Lehigh University, USA）
报告摘要：In this paper, we establish the quadratic convergence of Newton's method to the unique maximally complementary optimal solution of second-order conic optimization, when strict complementarity fails. Only very few approaches have been proposed to remedy the failure of strict complementarity, mostly based on nonsmooth analysis of the optimality conditions. Our local convergence result depends on the optimal partition of the problem, which can be identifi ed from a bounded sequence of interior solutions. We provide a theoretical complexity bound for identifying the quadratic convergence region of Newton's method from the trajectory of central solutions.