Equality Constraint

Equality constraints in optimization problems, aiming to find optimal solutions while satisfying specific restrictions, are a central focus in numerous scientific fields. Current research emphasizes efficient algorithms for incorporating these constraints, particularly within linear-quadratic regulator problems and neural network architectures like physics-informed neural networks, often leveraging techniques like Lagrangian multipliers and projection layers. These advancements improve the accuracy and efficiency of solving complex optimization tasks, with applications ranging from process control in chemical engineering to machine learning model training. The development of provably optimal constraint enforcement methods is a key area of ongoing investigation, aiming to guarantee constraint satisfaction while maintaining computational tractability.