Plancherel measure: Difference between revisions

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{{Infobox software
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| name                  = WORHP
| logo                  = [[File:Worhp 933x581.png|250px]]
| screenshot            =
| caption                =
| developer              = [http://www.math.uni-bremen.de/zetem/ChristofBueskens Christof Büskens], [http://www.unibw.de/lrt1/gerdts/mitarbeiter/prof.-gerdts Matthias Gerdts] et al.
| released              = {{Start date and age|df=yes|2010|03}}
| latest release version = 1.1
| latest release date    = {{Start date and age|2013|05|07|df=yes}}
| programming language  = [[ANSI C]], [[Fortran#FORTRAN_77|FORTRAN 77]], [[Fortran#Fortran_95|Fortran 95]] and [[Fortran#Fortran_2003|Fortran 2003]]
| operating system      = [[Unix-like]], [[Windows XP]] and later
| language              = [[English language|English]]
| genre                  = [[Numerical software]]
| license                = [[Proprietary software|Proprietary]], Free of charge for academic users.
| website                = [http://www.worhp.de worhp.de]
}}


'''WORHP''', pronounced like the English word "[[warp]]", also referred to as '''eNLP''' (European [[Nonlinear programming|NLP]] solver) by [[ESA]], is a mathematical software [[Library (computing)|library]] for solving continuous large scale [[nonlinear optimization]] problems numerically. The acronym WORHP is sometimes spelled out as "'''W'''e '''O'''ptimize '''R'''eally '''H'''uge '''P'''roblems", its primary intended application. WORHP is a hybrid [[Fortran#Fortran_2003|Fortran]] and [[C (programming language)|C]] implementation and can be used from C/[[C++]] and Fortran programs using different interfaces of varying complexity and flexibility. In addition interfaces for the modelling environments [[MATLAB]], [[CasADi]] and [[AMPL]] exist.<ref name="Interfaces">
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{{cite web |url=http://worhp.de/content/interfaces |title=WORHP interfaces}}
</ref>
 
== Problem formulation ==
WORHP is designed to solve problems of the form
::: <math>\min_{x \in \R^n} f(x)</math>
:subject to
::: <math>L \leq \begin{pmatrix} x \\ g(x) \end{pmatrix} \leq U </math>
with sufficiently smooth functions <math>f:\R^n \to \R</math> (objective) and <math>g:\R^n \to \R^m</math> (constraints) that may be nonlinear, and need not necessarily be convex. Even problems with large dimensions <math>n</math> and <math>m</math> can be solved efficiently, if the problem is sufficiently sparse.
Cases where objective and constraints cannot be evaluated separately, or where constraints can be evaluated element-wise can be exploited by WORHP to increase the computational efficiency.
 
=== Derivatives ===
WORHP requires the first [[derivative]] ([[Gradient]]) of <math>f</math> and of <math>g</math> ([[Jacobian_matrix_and_determinant|Jacobian]]) and second derivatives ([[Hessian matrix]]) of the [[Lagrange function]]; in a modelling environment like AMPL, these are provided by [[automatic differentiation]] methods, but need to be provided by the caller in other environments. First and second derivatives can be approximated by WORHP using [[finite differences]]. To reduce the otherwise prohibitively high number of necessary function evaluations in large scale [[sparse matrix|sparse]] problems, [[graph colouring]] theory is used to group first and second partial derivatives. Second derivatives may also be approximated using variations of the classic [[BFGS method]], including block-diagonal or sparse BFGS matrices.
 
== Structure ==
The NLP level of WORHP is based on [[Sequential quadratic programming|SQP]], while the quadratic subproblems are solved using an [[interior point method]]. This approach was chosen to benefit from the robustness of SQP methods and the reliable runtime complexity of IP methods, since traditional [[active set]] methods may be unsuitable for large-scale problems.
 
== Development ==
Development of WORHP started in 2006 with funding from [[German Aerospace Center|DLR]] and was continued under the ''eNLP'' label after 2008 with support by ESA / [[European Space Research and Technology Centre|ESTEC]] together with the Interior-Point solver ipfilter<ref name="ipfilter">
{{cite web |url=http://www.mat.uc.pt/ipfilter |title=ipfilter — An NLP Solver based on a primal-dual interior-point filter algorithm |author=Luis Vicente, Renata Silva, Michael Ulbrich, Stefan Ulbrich}}
</ref>
(whose inclusion in eNLP was discontinued after 2010) to develop a European NLP solver for use in trajectory optimisation, mission analysis and aerospace applications in general.<ref name="eNLP talk">
{{cite web |url=http://uma.ensta.fr/itn-sadco/?module=conf_aero&action=programme |title=eNLP: application-centric NLP-based optimization in the aerospace market  |location=ITN Sadco First Industrial Workshop |author=Sven Erb |date=2011-03-02}}
</ref>
 
The development of WORHP is led by the [http://www.stw.de/su/1118 Steinbeis-Forschungszentrum Optimierung, Steuerung und Regelung] and scientists of the [http://www.math.uni-bremen.de/zetem/o2c/en Optimization and Optimal Control Group] at the [[University of Bremen]], and at the [[Bundeswehr University of Munich]].<ref name="Development Team">
{{cite web |url=http://worhp.de/content/team-worhp |title=Development Team |accessdate=2013-05-27}}
</ref>
The developers stress that WORHP, despite its academic roots, is intended as industrial-grade tool rather than an academic research platform.<ref name="The ESA NLP Solver WORHP">
{{cite web |url=http://link.springer.com/chapter/10.1007%2F978-1-4614-4469-5_4 |author=Christof Büskens, Dennis Wassel |title=The ESA NLP Solver WORHP |accessdate=2013-05-27}}
</ref>
 
== Applications ==
WORHP has been integrated into trajectory analysis tools such as LOTNAV<ref name="LOTNAV">
{{cite web |url=http://adsabs.harvard.edu/abs/2004ESASP.548..609C |title=Navigation and Guidance for Low-Thrust Trajectories, LOTNAV  |author=J. L. Cano, M. Bello, J. Rodriguez-Canabal |year=2004}}
</ref>
and [[ASTOS]], and is being used at [[European Space Operations Centre|ESOC]] and [[European Space Research and Technology Centre|ESTEC]]. It can be used as optimiser in CasADi (since version 1.5.0beta)<ref name="CasADi">
{{cite web |url=https://github.com/casadi/casadi/wiki |title=CasADi wiki |accessdate=2013-05-27}}
</ref>
and as local optimiser in SVAGO MDO<ref name="SVAGO">
{{cite web |url=http://www.aero.polimi.it/~castellini |title=PRESTIGE MDO research, Research Achievements |author=Francesco Castellini |year=2009 |accessdate=2011-03-23}}
</ref> tool developed at University of Bremen and [[Politecnico di Milano]] on [[Multidisciplinary design optimization]] through the ESA PRESTIGE program.<ref name="PRESTIGE">
{{cite web|url=http://www.esa.int/esaMI/Education/SEM3E4WX3RF_0.html |title=Universities selected for PRESTIGE programme |author=ESA education |year=2009 |accessdate=2011-03-23}}
</ref>
 
== References ==
{{Reflist}}
 
== External links ==
* [http://www.worhp.de WORHP home page]
* [http://link.springer.com/chapter/10.1007%2F978-1-4614-4469-5_4 WORHP overview chapter]
 
 
{{Mathematical optimization software}}
[[Category:Mathematical optimization software]]
[[Category:Mathematical software]]
[[Category:Numerical software]]

Latest revision as of 15:52, 3 October 2014

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