Constrained Convex Optimization

Constrained convex optimization focuses on finding the minimum or maximum of a convex function subject to constraints, a fundamental problem across numerous scientific fields. Current research emphasizes developing efficient algorithms, particularly for large-scale and distributed settings, with a focus on methods like primal-dual algorithms, alternating direction method of multipliers (ADMM), and accelerated first-order methods, often tailored to specific constraint types or problem structures (e.g., simplex constraints, compositional covariates). These advancements are crucial for tackling real-world challenges in areas such as machine learning (including federated learning and distributed regression), signal processing (e.g., hyperspectral image fusion), and control systems, where data privacy and computational efficiency are paramount. The development of robust and scalable algorithms with strong theoretical guarantees continues to drive progress in this active research area.