DEPARTMENT OF APPLIED MATHEMATICS 92 Email tk.pong@polyu.edu.hk Qualification BSc (The Chinese University of Hong Kong) MPhil (The Chinese University of Hong Kong) PhD (University of Washington) ORCID ID 0000-0001-5862-2986 Dr PONG Ting-kei Associate Professor Research Overview Research Area: Continuous Optimisation Many problems that arise in contemporary applications such as compressed sensing and statistical learning can be formulated as structured optimisation problems. These problems involve minimising a loss function for data misfit together with a (or multiple) regulariser(s) for inducing desirable structure(s) in the solutions. Depending on the loss functions and regularisers, the optimisation problems that arise can be either convex or nonconvex; moreover, these problems usually involve billions of variables. My current research centres around the development and analysis of efficient algorithms for solving these structured optimisation problems. Given the size of the problems, my research primarily focuses on first-order methods: these algorithms mainly make use of first-order information such as gradients or the so-called proximal mapping of functions. As many important models in statistical learning are nonconvex, my current research focus is to develop and analyse methods for these nonconvex optimisation problems. Representative Publications • Kurdyka-Łojasiewicz exponent via inf-projection (with Guoyin Li and Peiran Yu) Found. Comput. Math. 22, 2022, pp. 1171–1217 • Convergence rate analysis of a sequential convex programming method with line search for a class of constrained differenceof-convex optimization problems (with Zhaosong Lu and Peiran Yu) SIAM J. Optim. 31, 2021, pp. 2024-2054 • Analysis and algorithms for some compressed sensing models based on L1/L2 minimization (with Peiran Yu and Liaoyuan Zeng) SIAM J. Optim. 31, 2021, pp. 1576-1603 • Calculus of the exponent of Kurdyka-Łojasiewicz inequality and its applications to linear convergence of first-order methods (With Guoyin Li) Found. Comput. Math. 18, 2018, pp. 1199-1232 • Douglas-Rachford splitting for nonconvex optimization with application to nonconvex feasibility problems (with Guoyin Li) Math. Program. 159, 2016, pp. 371-401 • Global convergence of splitting methods for nonconvex composite optimization (with Guoyin Li) SIAM J. Optim. 25, 2015, pp. 2434-2460
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