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.
KeywordsNonlinear optimization Large-scale Mathematical optimization NLP
The authors are indebted to Florian Wolff for his support in preparing the numerical results and for various suggestions on the manuscript and to Dr. Matthias Knauer for guiding the numerical evaluation with first TransWORHP results.
Development of WORHP has been supported by BMWi (German Federal Ministry of Economics and Technology) grants 50RL0722 and 50JR0688, the TEC-EC Control Division of the European Space Agency (ESA) in the projects eNLP (GSTP-4 G603-45EC) and eNLPext (GSTP-5 G517-045EC), and Steinbeis Research Center (SFZ) Optimization and Optimal Control.
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