SQP Methods for Parametric Nonlinear Programming

Dr. Vyacheslav Kungurtsev

Agent Technology Center, Department of Computer Science, Faculty of Electrical Engineering, Czech Technical University, Prague

Monday, June 30, 2014, 10:15 - 11:00

Room 01-016, Georges-Koehler-Allee 101, Freiburg 79110, Germany

Nonlinear Model Predictive Control (NMPC) requires the solution of a series of nonlinear programs (NLPs), each slightly different than the previous, at each receding horizon step. Sequential quadratic programming (SQP) is the prefered optimization approach for solving a series of related NLPs, because of its desireable “hot” and “warm” start properties. In particular, if the active set is the same, and certain other conditions hold, then a previous solution could correspond to the initial point of a Newton-like sequence of iteration. This ideal picture is, however, complicated by a) active set changes between the solution to each NLP b) the practical implementation of QP solvers, and c) situations in which standard strong assumptions do not hold. This talks discusses the details of the using second derivatives, which are ncessary for superlinear convergence, in algorithms for parametric nonlinear programming, as well as some theoretical and realized solutions to the challenges.