Optimization-based jailbreaking is an adversarial attack methodology used against artificial intelligence systems, particularly large language models, that employs automated mathematical optimization algorithms to generate inputs engineered to bypass safety guardrails and alignment filters. Unlike manual prompt engineering or social engineering attacks, this approach treats safety evasion as a formal optimization problem, systematically searching for token sequences or prompt suffixes that maximize the likelihood of the model producing restricted or harmful responses. The technique typically utilizes loss functions, model gradients, or discrete search heuristics to iteratively evaluate and update candidate tokens until the targeted model overrides its refusal behavior and fulfills the prohibited request.