(28g) A Parallel Interior Point Solver with Cyclic Reduction for Solving Large-Scale Dynamic Optimization Problems

Dynamic optimization problems directly incorporate detailed dynamic models as constraints within an optimization framework. Model predictive control, state estimation, and parameter estimation are all common applications of dynamic optimization. One dynamic optimization strategy, called direct transcription, is to discretize the continuous dynamics and replace the differential equations with algebraic approximations using some numerical method such as a finite-difference or Runge-Kutta (collocation) scheme. However, for problems with thousands of state variables and discretization points, discretization can lead to nonlinear optimization problems that exceed memory and speed limits of most serial computers. In particular, when applying interior point optimization methods, the computational bottleneck and dominant computational cost lies in solving the linear systems resulting from the Newton steps that solve the discretized optimality conditions. To overcome these limits, we exploit the parallelizable structure of the linear system to significantly accelerate the overall interior point algorithm. Our previous work has shown cyclic reduction (CR) to be a promising parallel linear solver for these problems. In this talk we extend this approach with an implementation of parallel CR within the open-source solver PIPS-NLP (Parallel Interior Point Solver for NLP). We demonstrate the effectiveness and scalability of the resulting optimization framework on several large-scale dynamic optimization applications including challenging distillation and polymerization systems.