Quadratic Objective

Quadratic objective functions are central to many optimization problems across diverse fields, from machine learning to robotics. Current research focuses on developing efficient algorithms to solve these problems, particularly in high-dimensional spaces and with constraints, employing techniques like semismooth-Newton methods, augmented Lagrangian methods, and evolutionary strategies. These advancements are improving the speed and scalability of optimization, impacting applications ranging from risk-aware decision-making and time-series analysis to the training of neural networks with improved robustness and performance. The development of faster algorithms for specific problem structures, such as those with low-rank factorizations or small treewidth, is a significant area of ongoing investigation.