Recent advances in storage, hardware, information technology, communication, and networking have resulted in a large amount of multimedia data. This has powered the demand to extract useful and actionable insights from such data in an automatic, reliable and scalable way. Machine learning, which aims to construct algorithms that can learn from and make predictions on data intelligently, has attracted increasing attention in the recent years and has been successfully applied to many multimedia computing tasks, such as image processing, face recognition, video surveillance, document summarization, etc. Since a lot of machine learning algorithms formulate the learning tasks as linear, quadratic or semi-definite mathematical programming problems, optimization becomes a crucial tool and plays a key role in machine learning and multimedia data analysis tasks. On the other hand, machine learning and the applications in multimedia computing are not simply the consumers of optimization technology but a rapidly evolving interdisciplinary research field that is itself promoting new optimization ideas, models, and solutions.