Convex Function Minimization

Convex function minimization, particularly in discrete settings, focuses on efficiently finding the input values that minimize a convex function. Recent research emphasizes developing and analyzing algorithms for online and offline minimization of L-convex and L^ℕ-convex functions, which generalize submodular functions to broader domains. A key trend involves leveraging machine-learned predictions to warm-start these algorithms, improving time complexity by focusing on the distance between predictions and the set of optimal solutions, even when multiple optima exist. These advancements have implications for various applications in operations research and machine learning, offering faster and more efficient solutions to complex optimization problems.