Constraint Violation

Constraint violation, the failure to satisfy predefined limitations in optimization or learning problems, is a central challenge across diverse fields, with research focusing on minimizing both the frequency and magnitude of violations while simultaneously optimizing the primary objective. Current efforts employ various techniques, including primal-dual methods, policy optimization in Markov Decision Processes (MDPs), and penalty-based gradient descent, often tailored to specific problem structures (e.g., linear or nonlinear constraints, stationary or non-stationary environments). Addressing constraint violation is crucial for developing robust and reliable algorithms in machine learning, control systems, and resource allocation, ensuring that solutions are not only optimal but also safe and feasible.