数学科学学院学术报告
A natural sequential quadratic programming method for nonlinear optimization
付文豪
（苏州科技大学）
报告时间：2024年7月12日 星期五 上午10：50-11：30
报告地点：沙河校区E404
报告摘要：The Sequential Quadratic Programming (SQP) method has shown remarkable performance in addressing nonlinear optimization problems. However, it typically requires the Quadratic Programming (QP) subproblems to be feasible. Various methods introducing QP subproblems with penalizations or perturbations have been developed to ensure feasibility. In this study, we present a natural SQP algorithm iterated by a stationary point of the classic QP subproblem, which is the minimizer closest to the feasible region. Feasibility for both the initial problem and the classic QP subproblem is not assumed. Under usual assumptions, the proposed algorithm globally converges to a solution with the least constraint violation. Specifically, the solution minimizes the objective function within the set of minimizers for the measure of constraint violation. Furthermore, the proposed method demonstrates a quadratic convergence rate. This approach is a natural extension of the classic SQP method. When the original problem is feasible, our assumptions and conclusions align with the classical SQP method. Numerical experiments validate the effectiveness and performance advantages of the proposed algorithm.
报告人简介：付文豪，讲师，2021年博士毕业于苏州大学，中国科学院访问学者，入选江苏省“双创博士”。主要研究领域为非线性规划、非线性半定规划的理论及其SQP型方法、最小约束违背优化及其应用等，当前感兴趣的课题是为潜在不可行的问题、带有非线性项的SDP问题提供有效算法。在《Optimization》、《International Journal of Numerical Analysis and Modeling》、《Acta Mathematicae Applicatae Sinica, English Series》等期刊上发表文章，指导数学建模竞赛并获奖10余项。
邀请人： 谢家新
