The Wasserstein barycenter problem seeks a probability measure that minimizes the weighted average of the Wasserstein distances to a given collection of probability measures. We study the discrete setting, where each measure has finite support — a regime that frequently arises in machine learning and operations research. The discrete Wasserstein barycenter problem is known to … Read more
In this paper, we study a penalty method for stochastic equality-constrained optimization, where both the objective and constraints are expressed in general expectation form. We introduce a novel adaptive strategy for updating the penalty parameter, guided by iteration progress to balance reductions in the penalty function with improvements in constraint violation, while each penalty subproblem … Read more
We present GFORS, a GPU-accelerated framework for large binary integer programs. It couples a first-order (PDHG-style) routine that guides the search in the continuous relaxation with a randomized, feasibility-aware sampling module that generates batched binary candidates. Both components are designed to run end-to-end on GPUs with minimal CPU–GPU synchronization. The framework establishes near-stationary-point guarantees for … Read more