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.