Ran Gu

Semi-discrete quadratic Wasserstein energy and state-dependent Langevin exploration

We study the semi-discrete quadratic Wasserstein energy. The energy is nonsmooth at collisions of sites. We prove local Lipschitz continuity on the full configuration space, together with global semiconcavity, coercivity, and dissipativity; show that every global minimizer is interior and collision free; and establish...

An Inexact Interior-Point Relaxation Method for Linear Optimization with a Spectral Preconditioner

Automatic Model-Order Selection for Nonnegative Matrix Factorization via Column $\ell_{2,0}$ Regularization

The critical points and local minimizers of the model are characterized, a sufficient-condition result for rank recovery is provided, and whole-sequence convergence of the proposed algorithms under explicit step-size and inertial-parameter conditions are proved using the Kurdyka--\L{}ojasiewicz framework.