Parametric Optimization

Parametric optimization focuses on efficiently finding optimal solutions to problems where the objective function and constraints depend on adjustable parameters. Current research emphasizes developing faster and more accurate solvers, particularly through machine learning approaches like neural networks trained using self-supervised learning and novel loss functions based on optimality conditions, or by integrating optimization layers directly into machine learning architectures using methods like Lagrangian Proximal Gradient Descent. These advancements are crucial for diverse applications, including real-time control systems, nanophotonic design, and the development of more efficient and robust algorithms across various scientific and engineering disciplines.