Zhou Jing
In order to further promote the internationalization of the School and actively promote the scientific research cooperation with research groups overseas, Professor Wang Song from Curtin University in Australia, at the invitation of the School of Mathematics, Physics and Statistics, gave a lecture entitled "Interior penalty method for finite-dimensional complementarity problems in Financial Engineering ". The presentation was moderated by Prof. Wang Guoqiang, Dean of the School of Mathematics, Physics and Statistics.
Starting from the finite-dimensional complementarity problem, Professor Wang explored the use of internal penalty function method to solve large-scale linear and nonlinear complementarity problems arising from the discretization of infinite-dimensional obstacle problems in classical and financial engineering. Secondly, Prof. Wang elaborated on the method of approximating the complementarity problem by nonlinear algebraic equations containing penalty/obstacle terms. To solve the penalty equation, Prof. Wang focused on a new smooth Newton method proposed by his research group, and showed that the linearized system can be reduced to two independent subsystems. In addition, he discussed the extended application of the method to other types of complementary problems.
The report verifies the convergence speed and accuracy of the proposed method by presenting numerical experimental results of several non-trivial test problems, and shares practical application cases of the method in the field of financial engineering. This lecture not only deepened the teachers and students' understanding of the penalty function method in solving finite dimensional complementarity problems, but also provided valuable insights into the research and application of related fields.
