This course prepares the engineer with advanced skills in the area of real-time optimisation for embedded systems. The course covers mathematical programming problem descriptions, necessary and sufficient conditions of optimality, duality, algorithm design and real-time considerations including early termination and warm-starting. The course covers special cases of linear programming, quadratic programming, convex programming and general smooth non-linear programming, slack variables and soft constraints as they arise in engineering problems. It also covers non-linear least squares problems with application to parameter estimation in dynamic systems, and integer programming and mixed-integer programming and their application to multi-agent task planning. The course has a particular emphasis on embedded systems applications where accuracy can be traded for speed.