Topic: An interior penalty method for finite-dimensional complementarity problems in Financial Engineering
Speaker:
Song Wang（汪崧）教授，澳大利亚科廷大学（Curtin University）数学与统计系教授。1982年在武汉大学获得学士学位，1989年在爱尔兰都柏林圣三一学院（Trinity College Dublin）获得博士学位，曾在爱尔兰都柏林的高科技公司--Tritech有限公司工作，先后任澳大利亚新南威尔士大学，科廷科技大学和西澳大利亚大学教授。主要从事偏微分方程的数值解，数值优化和最优控制，金融衍生品定价模型的理论和数值算法等研究。在SIAM Journal of Optimization, SIAM Journal of Numerical Analysis, Numerische Mathmatik, Automatica, IEEE Transactions on Neural Networks, IMA Journal of Numerical Analysis, Reports on Progress in Physics, Journal of Computational Physics, Biomaterial, Journal of Optimization Theory and Applications, Journal of Global Optimization等国际SCI知名杂志上发表学术论文150余篇。同时，汪教授还担任多个国际知名SCI杂志的主编，副主编以及编委。
Introduction:
In this work we propose and analyse an interior-point based penalty method for a finite-dimensional large-scale linear and nonlinear complementarity problem (CP) arising from the discretization of an infinite-dimensional obstacle problem in classic and financial engineering. In this approach, we approximate the CP by a nonlinear algebraic equation containing a penalty/barrier term with a penalty parameter mu. The penalty equation is shown to be uniquely solvable. We also prove that the approximate solutions converge to the exact one. A smooth Newton method is proposed for solving the penalty equation and it is shown that the linearized system is reducible to two decoupled subsystems. Extensions of this method to other types of CPs are will also be presented. Numerical experimental results using some non-trivial test problems will be presented to demonstrate the rates of convergence and accuracy of our methods.
Time: 2024.6.22 9:00
Lecture Location: 行政楼1308