Hi! Currently, I am a PhD candidate in the Department of Mathematics at the University of Hong Kong, supervised by Dr Yue Xie and Prof Zhiwen Zhang. Here is my CV.

Research overview

My research interests lie in mathematical optimization, particularly algorithms and theory.

Previously, we focused on nonsmooth composite optimization problems. We proposed a novel two-metric projection algorithm for $\ell_1$-norm regularization problems, which significantly improves the numerical performance of previous extensions of two-metric projection methods from bound constraints to $\ell_1$-norm regularization.

Currently, we study optimality (regularity) conditions for partly smooth functions. Partial smoothness is an important notion in optimization, connecting differential and variational geometry and providing a foundation for classical ideas such as active sets, sensitivity analysis, and optimality conditions. For the error bound condition, a widely used regularity condition in the convergence analysis of optimization algorithms, we provide a metric and geometric perspective. We show that, under a nondegeneracy condition, the error bound property is equivalent in the ambient space and on the active manifold associated with partial smoothness.

To further understand degenerate cases, we are exploring stratification theory as a possible framework.

Here is the introduction to part of my research slide.