Interviews with Faculty Researchers

– Interview with Dr Pong Ting-kei
Associate Professor, Department of Applied Mathematics

Algorithms – sets of instructions that computers can perform automatically – are becoming ubiquitous in modern society, from advertising to healthcare and even self-driving cars. More and more data-driven tasks are being optimised in the hope of making life easier, simpler and more efficient. In principle, optimisation algorithms take a complex practical problem and find the best solution under certain constraints. In practice, however, it can be extraordinarily difficult to solve such problems, because there are so many variables to consider and constraints to satisfy. This makes the design of solution methods (algorithms) challenging.

The research of Dr Pong Ting-kei, Associate Professor of the Department of Applied Mathematics, focuses on large-scale optimisation problems. “In modern applications,” notes Dr Pong, “optimisation problems that arise can involve billions of variables.” For example, delivery companies may wish to determine the best ways to deliver packages (e.g. to minimise fuel cost or waiting time) while maintaining only a limited number of vehicles. Given the complexity of today’s delivery and logistics networks, however, calculating the cost or time taken for every combination of vehicles, routes and customers is likely to require more computational power than currently available.

Dr Pong deploys his expertise in optimisation modelling and data science to streamline the solution process both mathematically and in real-world application scenarios, focusing on modern signal processing and machine learning applications. He studies certain properties of optimisation models that shed light on the convergence behaviour of existing algorithms. For example, the Kurdyka-Łojasiewicz property can be used to analyse how quickly a certain kind of algorithm converges to a solution. Understanding these properties enables Dr Pong to improve on existing models. “We can then develop more efficient algorithms with better empirical performance in terms of both runtime and solution quality,” he explains.

This research has implications for practitioners seeking solutions to complex, large-scale problems in fields as diverse as healthcare and communications. “One source of applications is the compressed sensing problem,” says Dr Pong. Compressed sensing algorithms can efficiently acquire and reconstruct a signal from just a few measurements. In the context of medical imaging, this allows practitioners to obtain high-resolution CT scans while minimising patients’ exposure to radiation. Such enhanced algorithms also offer tremendous potential in areas such as facial recognition, radar imaging and video processing.

分析與發展優化演算法

– 龐鼎基博士專訪
應用數學系副教授

演算法就是電腦可自動執行的指令集，在現代社會中，不論是廣告、醫療保健，甚至自動駕駛汽車都需要運用演算法，足跡可謂無處不在。越來越多數據為本的任務都透過演算法進行優化，務求令生活更輕鬆、簡單和有效率。原則上，優化演算法用來應對複雜的優化問題，意指在某些限制下找出最佳解決方案。然而在實踐方面，由於有太多變量需要考慮，亦有太多限制條件需要滿足，解決此類問題往往會面對難以想像的困難，令設計解決方法（演算法）更具挑戰性。

應用數學系副教授龐鼎基博士主要研究大規模優化問題。他表示：「在現代應用中，優化問題可能涉及數十億個變量。」例如，速遞公司或會希望找出運送包裹的最佳方式，一方面能減少燃料開支或等待時間，另一方面可以為車隊組成數目設限。然而，當今速遞和物流網路異常複雜，要計算車輛、路線和客戶每個組合所需的成本或時間，現有電腦的計算能力或許未能勝任。

龐博士憑藉其優化建模和數據科學的專業知識，以數學方式研究現代訊息處理和機器學習涉及的優化問題。他研究了優化模型的某些屬性，揭示了現有演算法的收斂性質。例如，Kurdyka-Łojasiewicz條件，便可用作分析某些演算法收斂至找出解決方法的速度。龐博士可透過相關性質改進現有模型。他解釋道：「接下來，我們可以開發更有效的演算法。」

對於致力為複雜而大規模問題尋找解決方法的人來說，這些研究於醫療保健及傳訊方面意義重大。龐博士表示：「這些理論可用來為壓縮傳感問題設計更好的算法。」壓縮傳感演算法可以有效地從少量測量中採集和重建信號。在醫學成像的領域，醫護人員可以以此獲得高解像度的電腦斷層掃描，同時盡量減少患者接觸放射性物質。此類加強的演算法在面部識別、雷達成像和視頻處理等領域也有巨大潛力。