Title: | Confirmation of Candidature Seminar: Kernel-based methods for solving partial differential equations on moving B-spline surface |
Speaker: | Mr AMMAD Muhammad, Department of Mathematics, Hong Kong Baptist University, Hong Kong |
Time/Place: | 15:00 - 15:45 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | This project aims to develop efficient algorithms for solving PDEs on B-spline surfaces, focusing on accurate estimation of surface normal and curvature. The algorithms will improve computational efficiency by using the mathematical formulations and structures of B-spline surfaces. Additionally, the project aims to extend the algorithms to solve PDEs on evolving surfaces, allowing for fast solution updates based on user-defined control points. The expected results include visualizations of the numerical solution, demonstrating surface evolution and deformation. The developed algorithms have broad applications in modeling and simulating systems governed by PDEs with moving components. |
Title: | Confirmation of Candidature Seminar: Intrinsic Meshfree Methods for Surface PDEs on Manifolds |
Speaker: | Ms SU Yichen, Department of Mathematics, Hong Kong Baptist University, Hong Kong |
Time/Place: | 15:45 - 16:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | In the realm of solving surface PDEs defined on manifolds, existing approaches such as embedding methods and projection methods have made significant contributions. However, to further advance the field, our upcoming research will primarily focus on the development of a local intrinsic method. This approach aims to capture the geometric characteristics more effectively, offering a promising alternative for solving surface PDEs on manifolds. Additionally, we will explore the combination of this method with Kernel-based approaches for solving PDEs. Moreover, we will incorporate the least-square radius basis function finite difference (RBF-FD) method into our proposal, capitalizing on its flexibility with irregular domains, particularly on point clouds. |
Title: | Confirmation of Candidature Seminar: An new preconditioning for linear system from a space fractional diffusion equation |
Speaker: | Ms DONG Jiamei, Department of Mathematics, Hong Kong Baptist University, Hong Kong |
Time/Place: | 16:30 - 17:15 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | In this work, we propose a simple preconditioned Krylov subspace method for a non-symmetric block Toeplitz all-at-once system, which arises from the discretization of the space fractional diffusion equation. Our main result is a novel symmetric positive definite preconditioner, which can be efficiently diagonalized by the discrete sine transform matrix. Specifically, our approach is to first permute the original linear system to obtain a symmetric one. Then, using the hermitian part of the coefficient matrix, we constructed the τ preconditioner. Numerical examples are given in order to demonstrate the efficiency of our method for the preconditioner. |
Title: | Confirmation of Candidature Seminar: Neyman-Pearson Classifier with Successive Convex Approximation |
Speaker: | Mr ZHANG Hao, Department of Mathematics, Hong Kong Baptist University, Hong Kong |
Time/Place: | 17:15 - 18:00 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | The task of binary classification and prediction has been a significant focus of research due to its wide application. For the priority of the classification accuracy of a particular class, the Neyman-Pearson (NP) paradigm is developed to control the classification error of the prioritized class under a pre-specified level. The splitting of samples serves a vital role for most of the existing NP classifiers, which ensures control of the prioritized class with a high chance. The limitation of excluding a proportion of samples from the training procedures provides motivation for proposing a novel algorithm that addresses these drawbacks. In order to maximize the utilization of all available samples, we propose a new classifier from an empirical optimization perspective. Under the linear discriminant analysis assumption, we leverage the difference-of-convex approximation and successive convex approximation to solve the classification problem with the NP paradigm. Our method has the capability to control the classification error of the prioritized class both at the sample and population levels. By incorporating a penalty term within the algorithm, we can ensure that the error is controlled with a probability of 1. Numerical study and real-world applications demonstrate the effectiveness of the proposed method. |
Title: | Utility Preference Robust Optimization with Moment-Type Information Structure |
Speaker: | Dr. Sainan Zhang, Department of Systems Engineering and Engineering Management, CUHK |
Time/Place: | 14:30 - 15:30 FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University |
Abstract: | Utility preference robust optimization (PRO) models have recently been proposed to deal with decision-making problems where the decision-maker’s true utility function is unknown and the optimal decision is based on the worst-case utility function in an ambiguity set of utility functions. In this paper, we consider the case where the ambiguity set is constructed using some moment-type conditions. We propose piecewise linear approximation of the utility functions in the ambiguity set. The approximate maximin problem can be solved directly by derivative-free methods when the utility functions are nonconcave. Alternatively, we can reformulate the approximate problem as a single mixed integer linear program (MILP) and solve the MILP by existing solvers such as Gurobi. To justify the approximation scheme, we derive error bounds for the approximate ambiguity set, the optimal value and optimal solutions of the approximate maximin problem. To address the data perturbation/contamination issues arising from the construction of the ambiguity set, we derive some stability results which quantify the variation of the ambiguity set against perturbations in the elicitation data and its propagation to the optimal value and optimal solutions of the PRO model. Moreover, we extend the PRO models to allow some inconsistencies in the process of eliciting the decision-maker’s preferences. Finally, we carry out numerical tests to evaluate the performances of the proposed numerical schemes and show that the computational schemes work fairly efficiently, the PRO model is resilient against small perturbations in data (with respect to both exogenous uncertainty data and preference elicitation data), and there is a potential to improve the efficiency of the preference elicitation by incorporating an optimal selection strategy. |
We organize conferences and workshops every year. Hope we can see you in future.
Learn MoreProf. M. Cheng, Dr. Y. S. Hon, Dr. K. F. Lam, Prof. L. Ling, Dr. T. Tong and Prof. L. Zhu have been awarded research grants by Hong Kong Research Grant Council (RGC) — congratulations!
Learn MoreFollow HKBU Math