学术报告会：An adaptive cubic regularisation method for nonlinear equality constrained optimization

报告题目：An adaptive cubic regularisation method for nonlinear equality constrained optimization

报 告 人： 裴永刚  （河南师范大学 副教授）

报告时间：2024年10月12日周六11：00

报告地点：S3-313

Abstract：The adaptive regularisation algorithm using cubics (ARC) is initially proposed for unconstrained optimization. ARC has excellent convergence properties and complexity. In this talk, we extend ARC to solve nonlinear constrained optimization and propose a class of sequential adaptive regularisation using cubics algorithms inspired by sequential quadratic programming (SQP) methods. In each iteration of our method, the trial step is computed via composite-step approach, i.e., it is decomposed into the sum of normal step and tangential step. By means of reduced-Hessian approach, a new ARC subproblem for nonlinear equality constrained optimization is constructed to compute the tangential step, which can supply sufficient decrease required in the proposed algorithm. Once the trial step is obtained, the ratio of the penalty function reduction to the model function reduction is calculated to determine whether the trial point is accepted. The global convergence of the algorithm is investigated under some mild assumptions. Preliminary numerical experiments are reported to show the performance of the proposed algorithm.

个人简介：

裴永刚，男，博士，河南师范大学数学与信息科学学院副教授、研究生导师，副院长，河南省运筹学会副秘书长。主要从事非线性优化计算方法的理论与应用研究，在Computational Optimization and Applications、Journal of Computational and Applied Mathematics、Acta Mathematica Sinica, English Series、Numerical Algorithms 等期刊上发表学术论文20 余篇。承担国家自然科学基金项目、省级重点科研项目多项，获省自然科学优秀学术论文一等奖1项。