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 under
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The ESA NLP Solver WORHP Christof B€ uskens and Dennis Wassel
Abstract 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. Keywords Nonlinear optimization • Large-scale • Mathematical optimization • NLP
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Introductory Remarks
Nonlinear optimization has grown to a key technology in many areas of aerospace industry, especially for solving discretized optimal control problems with differential equation systems, like ordinary differential equations (ODEs),
C. B€uskens (*) • D. Wassel Center for Industrial Mathematics, University of Bremen, Bremen, Germany e-mail: [email protected]; [email protected] G. Fasano and J.D. Pinte´r (eds.), Modeling and Optimization in Space Engineering, Springer Optimization and Its Applications 73, DOI 10.1007/978-1-4614-4469-5_4, # Springer Science+Business Media New York 2013
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differential-algebraic equations (DAEs), and partial differential equations (PDEs). Applications are satellite control, shape-optimization, aerodynamics, trajectory planning, reentry problems, and interplanetary flights. One of the most extensive areas is the optimization of trajectories for aerospace applications; this book is proof to that notion. Nonlinear optimization problems arising from these applications typically are large and sparse. Previous methods for solving nonlinear optimization problems were originally developed for small- to medium-sized1 and dense problems. Many challenging optimization problems cannot be tackled by these solvers due to their size. Solving large-scale problems requires an NLP solver to exploit as much of the problem structure as possible. This implies efficient storage of sparse vectors and matrices, special linear algebra methods for solving sparse, large-scale linear systems of equations and efficient methods for approximation of sparse first and second derivatives. Most of the available optimi
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