Approximately Optimal Utility Maximization

All opportunistic scheduling algorithms solve simpler optimization problems at each scheduling instance in order to achieve good long-term performance. The analysis of these algorithms assumes that the simpler optimization problems are solved exactly. However, in contrast, real-life implementations only approximately solve these problems but still yield close to optimal performance. We formalize this observation by explicitly bounding the long-term performance in terms of the error in the approximation made at every stage.