3 citations · 7 across the 8 of their papers we have counts for
8 papers
Local geometry of feasible regions via smooth paths
Adrian S. Lewis, Adriana Nicolae, Tonghua Tian
Variational analysis presents a unified theory encompassing in particular both smoothness and convexity. In a Euclidean space, convex sets and smooth manifolds both have straightfo…
Automated Essay Scoring in Argumentative Writing: DeBERTeachingAssistant
Yann Hicke, Tonghua Tian, Karan Jha +1
Automated Essay scoring has been explored as a research and industry problem for over 50 years. It has drawn a lot of attention from the NLP community because of its clear educatio…
The complexity of first-order optimization methods from a metric perspective
Adrian S. Lewis, Tonghua Tian
A central tool for understanding first-order optimization algorithms is the Kurdyka-Lojasiewicz inequality. Standard approaches to such methods rely crucially on this inequality to…
On the local convergence of the semismooth Newton method for composite optimization
Jiang Hu, Tonghua Tian, Shaohua Pan +1
In this paper, we consider a large class of nonlinear equations derived from first-order type methods for solving composite optimization problems. Traditional approaches to establi…
Identifiability, the KL property in metric spaces, and subgradient curves
Adrian Lewis, Tonghua Tian
Identifiability, and the closely related idea of partial smoothness, unify classical active set methods and more general notions of solution structure. Diverse optimization algorit…
The structure of conservative gradient fields
Adrian Lewis, Tonghua Tian
The classical Clarke subdifferential alone is inadequate for understanding automatic differentiation in nonsmooth contexts. Instead, we can sometimes rely on enlarged generalized g…
Ground states and their characterization of spin- Bose-Einstein condensates
Tonghua Tian, Yongyong Cai, Xinming Wu +1
The computation of the ground states of spin- Bose-Einstein condensates (BECs) can be formulated as an energy minimization problem with two quadratic constraints. We discretize…
Partial smoothness and constant rank
Adrian S. Lewis, Jingwei Liang
The idea of partial smoothness in optimization blends certain smooth and nonsmooth properties of feasible regions and objective functions. As a consequence, the standard first-orde…