ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
This paper concerns the implementation of a recent idea, attributed to Hestenes and Powell, based on solving the equality constrained finite dimensional minimization problem \documentclass{article}\pagestyle{empty}\begin{document}$$ \min \,\{ \,f(x)|(x)\, = \,0,\,x \in \,R^n \} $$\end{document} via the unconstrained problem \documentclass{article}\pagestyle{empty}\begin{document}$$ \min \,\{ f\,(x)\, + \, 〈 g(x),\,\lambda 〉 + 0.5 〈 g(x),\,Kg(x) 〉 \,|\,x\, \in \,R^n,\,\lambda \, \in \,R^p $$\end{document} where ƒ is a non-linear functional, g is a non-linear mapping into Rp, K is a prescribed matrix of penalty constants and λ is the Lagrange multiplier. The computational algorithm is based on restoring active constraints to first order and adjusting x in the remaining necessary conditions by gradient projection. The minimization is performed by the variable metric rank-two BGFS update with linear search by cubic interpolation. Computational results using the algorithm include two problems of minimum fuel trajectory optimization - two impulse rendezvous with Comet Encke and three impulse constrained positioning of a geostationary satellite.
Additional Material:
1 Tab.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620100506
Permalink
