报告人:Prof. Xin-wei Liu (Hebei University of Technology) 邀请人:袁亚湘研究员 时间:5月11日(星期二),上午 11:00-12:00 地点:科技综合楼 311 报告题目:A sequential quadratic programming method without a penalty function or a filter for nonlinear equality constrained optimization 摘要: We present a sequential quadratic programming method without using a penalty function or a filter for solving nonlinear equality constrained optimization. In each iteration, the linearized constraints of the quadratic programming are relaxed to satisfy two mild conditions, the step-size is selected such that either the value of the objective function or the measure of the constraint violations is sufficiently reduced. As a result, our method has two nice properties. Firstly, we do not need to assume the boundedness of the iterative sequence; Secondly, we do not need any restoration phase which is necessary for filter methods. We prove that the algorithm will terminate at either an approximate Karush-Kuhn-Tucker point or an approximate Fritz-John point, or an approximate infeasible stationary point which is an approximate stationary point for minimizing the $\ell_2$ norm of the constraint violations. By controlling the exactness of the linearized constraints and introducing a second-order correction technique, without requiring linear independence constraint qualification, the algorithm is shown to be locally superlinearly convergent. The numerical results show that the algorithm is robust and efficient.