Smooth Convex Optimization

Smooth convex optimization focuses on efficiently finding the minimum of a smooth, convex function, a fundamental problem across numerous scientific and engineering disciplines. Current research emphasizes developing and analyzing algorithms like stochastic gradient descent (SGD), accelerated gradient methods, and quasi-Newton methods, often incorporating techniques such as Richardson-Romberg extrapolation, distributed optimization strategies, and communication compression to improve convergence rates and scalability. These advancements are crucial for tackling large-scale problems in machine learning, signal processing, and other fields where efficient optimization is paramount, leading to improved algorithm performance and enabling the solution of previously intractable problems.