WORHP

WORHP, pronounced like the English word " warp", at ESA also known as " ENLP " (NLP solver ) is a mathematical program or a library for the numerical solution of continuous high-dimensional nonlinear optimization problems. The abbreviation WORHP means literally "We Optimize Really Huge problem ", this is the primary area of ​​application of the software dar. WORHP hybrid is implemented in Fortran and C, and also offers the option via different interfaces in C / C - and Fortran programs integrated to become. Additionally, there are interfaces for integration into the modeling environments MATLAB, Casadi and AMPL.

Formulation of the problem

WORHP was developed to address problems of the mold

To solve with sufficiently smooth functions ( objective function ) and (constraints ) that may be non-linear and do not have to be necessary convex. Even problems with very large dimensions, and can be solved efficiently, if the problem is sufficiently sparse; the highest achieved to date dimensions are on the order. Problems in which it is not possible to evaluate objective function and constraints separately, or in which it is possible to evaluate the constraints for each element can be exploited by WORHP to make the computation efficient.

Derivations

WORHP requires the first derivative (gradient ) of and ( Jacobian matrix ), and the second derivative (Hesse matrix) of the Lagrange function; in a modeling environment AMPL how this can be provided by automatic differentiation are available, but in other applications, these need to be passed by the user. First and second derivatives can be determined by WORHP using finite differences. To avoid the typically resulting very large number of function evaluations dimensional sparse applications graph coloring theory is utilized to group the first and second derivatives. Second derivatives can also be approximated by variations of the classical BFGS method, including block- diagonal and sparse variant. WORHP first implemented NLP method, a structure -preserving (ie possibly sparse ) SBFGS process, for which there is a proof of convergence.

Structure

In NLP level WORHP based on a classic SQP algorithm, whereas the quadratic subproblems are solved using interior-point method. This setup was chosen to take advantage of the resilience of SQP method and reliable numerical effort IP method, since conventional active set strategies are unsuitable for high dimensional problems.

Development

The development of WORHP launched in 2006 with a funding of the German Centre for Aerospace and was continued under the name " ENLP " after 2008 with the support of ESA / ESTEC, together with the interior-point solver ipfilter. Goal was to implement an NLP solver to determine optimal trajectories, mission analysis and for space applications in general. ( The use of Ipfilter in WORHP was not pursued after 2010. ) The Steinbeis Research optimization, control and regulation and scientists working group Optimization and Optimal Control at the University of Bremen and the University of the Federal Armed Forces Munich working on the further development of WORHP. The developers of WORHP emphasize that it was developed in spite of its academic origin from the outset as industrially usable tool rather than pure research platform.

Applications

WORHP was integrated into programs for the analysis of trajectories as LOTNAV and ASTOS, and is used at ESOC and ESTEC on. It is also possible to integrate WORHP as optimizer in Casadi ( since version 1.5.0 beta) and it is used as a local optimizer in Svago MDO program, developed at the University of Bremen and the Politecnico di Milano, for multidisciplinary optimization in the ESA PRESTIGE program.