The ESA NLP Solver WORHP. We Optimize Really Huge Problems (WORHP) is a solver for large-scale, sparse, nonlinear optimization problems with millions of variables and constraints. Convexity is not required, but some smoothness and regularity assumptions are necessary for the underlying theory and the algorithms based on it. WORHP has been designed from its core foundations as a sparse sequential quadratic programming (SQP) / interior-point (IP) method; it includes efficient routines for computing sparse derivatives by applying graph-coloring methods to finite differences, structure-preserving sparse named after Broyden, Fletcher, Goldfarb and Shanno (BFGS) update techniques for Hessian approximations, and sparse linear algebra. Furthermore it is based on reverse communication, which offers an unprecedented level of interaction between user and nonlinear programming (NLP) solver. It was chosen by ESA as the European NLP solver on the basis of its high robustness and its application-driven design and development philosophy. Two large-scale optimization problems from space applications that demonstrate the robustness of the solver complement the cursory description of general NLP methods and some WORHP implementation details.

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  1. Andersson, Joel A. E.; Gillis, Joris; Horn, Greg; Rawlings, James B.; Diehl, Moritz: CasADi: a software framework for nonlinear optimization and optimal control (2019)
  2. Andreani, Roberto; Ramirez, Viviana A.; Santos, Sandra A.; Secchin, Leonardo D.: Bilevel optimization with a multiobjective problem in the lower level (2019)
  3. Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Worthmann, Karl: Symmetry and motion primitives in model predictive control (2019)
  4. Kuhlmann, Renke: Learning to steer nonlinear interior-point methods (2019)
  5. Pernot, Jean-Philippe; Michelucci, Dominique; Daniel, Marc; Foufou, Sebti: Towards a better integration of modelers and black box constraint solvers within the product design process (2019)
  6. Kuhlmann, Renke; Büskens, Christof: A primal-dual augmented Lagrangian penalty-interior-point filter line search algorithm (2018)
  7. Kuhlmann, Renke; Geffken, Sören; Büskens, Christof: WORHP Zen: parametric sensitivity analysis for the nonlinear programming solver WORHP (2018)
  8. Magnusson, Fredrik; Åkesson, Johan: Symbolic elimination in dynamic optimization based on block-triangular ordering (2018)
  9. Müller, Benjamin; Kuhlmann, Renke; Vigerske, Stefan: On the performance of NLP solvers within global MINLP solvers (2018)
  10. do Rosário de Pinho, Maria; Nunes Nogueira, Filipa: On application of optimal control to SEIR normalized models: pros and cons (2017)
  11. Izzo, Dario; Hennes, Daniel; Simões, Luís F.; Märtens, Marcus: Designing complex interplanetary trajectories for the global trajectory optimization competitions (2016)
  12. Büskens, Christof; Wassel, Dennis: The ESA NLP solver WORHP (2013)
  13. Cremaschi, Francesco: Trajectory optimization for launchers and re-entry vehicles (2013)
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  15. Lantoine, Gregory; Russell, Ryan P.: A hybrid differential dynamic programming algorithm for constrained optimal control problems. I: Theory (2012)