Hard Inequality Constraint

Hard inequality constraints in optimization problems represent limitations that must be strictly satisfied, posing significant challenges for algorithm design. Current research focuses on developing efficient algorithms, such as primal-dual methods and adaptive regret minimization techniques, to handle these constraints within various frameworks, including bandits, variational inequalities, and neural network training. These advancements are crucial for addressing real-world problems in diverse fields like robotics, wireless network scheduling, and machine learning, where satisfying hard constraints is essential for system stability and performance. The development of robust and efficient methods for handling such constraints is a key area of ongoing research with broad implications across numerous scientific disciplines.