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Before the advent of computers around 1950, optimization centered either on small-dimensional problems solved by looking at zeroes of first derivatives and signs of second derivatives, or on infinite-dimensional problems about curves and surfaces. In both cases, "variations" were employed to understand how a local solution might be characterized. Computers changed the picture by opening the possibility of solving large-scale problems involving inequalities, instead of only equations. Inequalities had to be recognized as important because the decisions to be optimized were constrained by the need to respect many upper or lower bounds on their feasibility. A new kind of mathematical analysis, beyond traditional calculus, had to be developed to address these needs. It built first on appealing to the convexity of sets and functions, but went on to amazingly broad and successful concepts of variational geometry, subgradients, subderivatives, and variational convergence beyond just that. This talk will explain these revolutionary developments and why there were essential.
Event date: 1/11/2022
Speaker: Prof. Terry Rockafellar (University of Washington)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Computer science -- Mathematics Mathematical optimization Convex sets Convex functions
- Resource Type:
- Video
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Video
Geospatial information science is a discipline that focuses on using geospatial information technology to understand people, places, nature and processes of the earth. IoT refers to Internet of things, the combination of sensors, software and other technologies to connect and exchange data with other devices and systems over the Internet. The era of IoT brings us opportunities and challenges for geospatial information science. In the keynote, five characteristics and three scientific issues of geo-spatial information science in the era of IoT are summarised.
Event date: 06/09/2022
Speaker: Prof. Daren Li
Moderator: Prof. Christopher Chao (Hong Kong Polytechnic University)
Panel members: Prof. Qingyan Chen, Prof. Qinhao Chen (Hong Kong Polytechnic University)
Hosted by: PolyU Academy for Interdisciplinary Research
- Subjects:
- Land Surveying and Geo-Informatics
- Keywords:
- Spatial data mining Internet of things Geospatial data
- Resource Type:
- Video
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Video
Adaptive computation is of great importance in numerical simulations. The ideas for adaptive computations can be dated back to adaptive finite element methods in 1970s. In this talk, we shall first review some recent development for adaptive methods with some application. Then, we will propose a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. In particular, we propose the failure informed PINNs (FI-PINNs), which can adaptively refine the training set with the goal of reducing the failure probability. Compared with the neural network approximation obtained with uniformly distributed collocation points, the proposed algorithms can significantly improve the accuracy, especially for low regularity and high-dimensional problems.
Event date: 18/10/2022
Speaker: Prof. Tao Tang (Beijing Normal University-Hong Kong Baptist University United International College)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical models Differential equations Partial -- Numerical solutions Adaptive computing systems Sampling (Statistics)
- Resource Type:
- Video
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Video
Convex Matrix Optimization (MOP) arises in a wide variety of applications. The last three decades have seen dramatic advances in the theory and practice of matrix optimization because of its extremely powerful modeling capability. In particular, semidefinite programming (SP) and its generalizations have been widely used to model problems in applications such as combinatorial and polynomial optimization, covariance matrix estimation, matrix completion and sensor network localization. The first part of the talk will describe the primal-dual interior-point methods (IPMs) implemented in SDPT3 for solving medium scale SP, followed by inexact IPMs (with linear systems solved by iterative solvers) for large scale SDP and discussions on their inherent limitations. The second part will present algorithmic advances for solving large scale SDP based on the proximal-point or augmented Lagrangian framework In particular, we describe the design and implementation of an augmented Lagrangian based method (called SDPNAL+) for solving SDP problems with large number of linear constraints. The last part of the talk will focus on recent advances on using a combination of local search methods and convex lifting to solve low-rank factorization models of SP problems.
Event date: 11/10/2022
Speaker: Prof. Kim-Chuan Toh (National University of Singapore)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Semidefinite programming Convex programming
- Resource Type:
- Video
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Video
We introduce a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while using only Hessian-vector products in two directions. Moreover; the computational overhead remains comparable to the first-order such as the gradient descent method. We show that the method has a local super-linear convergence and a global convergence rate of 0(∈-3/2) to satisfy the first-order and second-order conditions under a commonly used approximated Hessian assumption. We further show that this assumption can be removed if we perform one step of the Krylov subspace method at the end of the algorithm, which makes DRSOM the first first-order-type algorithm to achieve this complexity bound. The applicability and performance of DRSOM are exhibited by various computational experiments in logistic regression, L2-Lp minimization, sensor network localization, neural network training, and policy optimization in reinforcement learning. For neural networks, our preliminary implementation seems to gain computational advantages in terms of training accuracy and iteration complexity over state-of-the-art first-order methods including SGD and ADAM. For policy optimization, our experiments show that DRSOM compares favorably with popular policy gradient methods in terms of the effectiveness and robustness.
Event date: 19/09/2022
Speaker: Prof. Yinyu Ye (Stanford University)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Nonconvex programming Mathematical optimization Convex programming
- Resource Type:
- Video
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Video
Machine learning can deliver unprecedented performance. Its application domain has expanded into safety-critical cyber-physical systems such as UAVs and self-driver cars. However, the safety assurance of vehicular control has two conditions: 1) an analytical model of system behaviors such as provable stability, and 2) the software safety certification process (e.g., DO 178C) requires that the software be simple enough so that software safety can be validated by a combination of model checking and near exhaustive testing. Although ML software, as is, does not meet these two safety requirements, the real-time physics model supervised ML architecture holds the promise to 1) meet the two safety requirements and 2) enable ML software to safely improve control performance and safely learn from its experience in real-time. This talk will review the structure of the proposed architecture and some methods to embed physics into ML-enabled CPS control.
Event Date: 12/05/2022
Speaker: Prof. Lui Sha (University of Illinois Urbana-Champaign)
Hosted by: Graduate School
- Subjects:
- Computing, Data Science and Artificial Intelligence and Aeronautical and Aviation Engineering
- Keywords:
- Machine learning Computer software -- Reliability Drone aircraft Vehicles Remotely piloted
- Resource Type:
- Video
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Video
The textile and fashion industry is in troubled times. Hong Kong is no exception. Our traditional market, the US, while difficult since 2018, has been dire in the covid pandemic. The industry is in the mist of disruptive changes brought by technological revolutions, in particular digitalization, and the retreat of globalism. But troubles always come with opportunities. Dr Henry Tan will give an overview on the outlook of the industry and his view on where opportunities are knocking.
Event date: 25/02/2021
Speaker: Dr Henry Tan (CEO, Luen Thai Group Ltd)
Hosted by: Institute of Textiles and Clothing
- Subjects:
- Fashion retailing and merchandising
- Keywords:
- Clothing trade -- China -- Hong Kong Clothing trade -- Technological innovations
- Resource Type:
- Video
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Video
Ms Shirley Chan, BBS, JP, Vice Chairman of YGM Trading Ltd. shared her insights on the trend of global fashion supply chain under the "New Normal".
Event date: 24/11/2020
Speaker: Ms Shirley Chan (Vice Chairman, YGM Trading Limited)
Facilitators: Dr Chris Lo (ITC), Dr Fan Di (ITC)
Hosted by: Institute of Textiles and Clothing
- Subjects:
- Fashion retailing and merchandising
- Keywords:
- Clothing trade COVID-19 Pemic (2020-) Clothing trade -- Technological innovations
- Resource Type:
- Video
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Video
Air transport liberalisation has been marked by two major developments, i.e. the advent of the hub-and-spoke network and the emergence of Low Fare Airlines (LFAs). All major Full Service Network Carrier (FSNCs) have heavily relied on hub operations to effectively compete in the long-haul market against LFAs which until recently focused on point-to-point, short-haul services. Recent competiton dynamics, however, have led to the gradual blurring of the different airline business models. LFAs have now established strong bases in satellite/airports and/or in low-cost terminals of major airports. Moreover, they have introduced long-haul flights thus competing with FSNCs at a new level. The lecture will highlight all the above issues focusing on their strategic business and geopolitical implications for aiport hubs. It will also discuss how Hong Kong International Airport can build on its current advantages to play focal role in the new environment.
Event Date: 16/06/2017
Speaker: Prof. Andreas Papatheodorou (University of Aegean)
Hosted by: School of Hotel and Tourism Management
- Subjects:
- Hotel, Travel and Tourism
- Keywords:
- Airlines -- Rates Airports Hong Kong International Airport Aeronautics Commercial
- Resource Type:
- Video
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Video
Using UC Berkeley as an exemplar, Prof. Koshland gave us a distinguished lecture on ‘Lighting the Way with Interdisciplinary Research since 1868’. One of the hallmarks of UC Berkeley has always been engagement of its faculty and students in research and education that expand in cross disciplines, joining on multiple approaches to address major challenges facing the world today, which is also what we are seeking to do at PAIR of PolyU. Moreover, Prof. Koshland shared with us the ways in which individuals and institutions can engage in interdisciplinary and multi-disciplinary research and education and how they can be creatively intertwined.
Event Date: 22/4/2022
Speaker: Prof. Catherine P. Koshland (University of California, Berkeley)
Moderator: Prof. Christopher Chao (Hong Kong Polytechnic University)
Panel members: Prof. Xiang-dong Li, Prof. Yuguo Li (Hong Kong Polytechnic University)
Hosted by: PolyU Academy for Interdisciplinary Research
- Keywords:
- Interdisciplinary research Interdisciplinary approach in education
- Resource Type:
- Video