講座題目 | An interior penalty method for finite-dimensional complementarity problems in Financial Engineering | ||
主辦單位 | 數理與統計意昂2 | 協辦單位 | 應用統計系 |
講座時間 | 6月22日09:00-10:00 | 主講人 | Song Wang （汪崧） |
講座地點 | 行政樓1308室 | ||
主講人簡介 | Song Wang（汪崧）教授，澳大利亞科廷大學（Curtin University）數學與統計系教授。1982年在武漢大學獲得學士學位🧑🏻✈️，1989年在愛爾蘭都柏林聖三一意昂2（Trinity College Dublin）獲得博士學位，曾在愛爾蘭都柏林的高科技公司--Tritech有限公司工作，先後任澳大利亞新南威爾士大學，科廷科技大學和西澳大利亞大學教授👵🏿。主要從事偏微分方程的數值解，數值優化和最優控製，金融衍生品定價模型的理論和數值算法等研究🫃🏽🪅。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等國際SCI知名雜誌上發表學術論文150余篇🧙🏿♂️。同時🕧，汪教授還擔任多個國際知名SCI雜誌的主編，副主編以及編委👨🚀。 | ||
講座內容簡介 | 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. | ||