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Title of Journal: J Geod

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Abbravation: Journal of Geodesy

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Publisher

Springer Berlin Heidelberg

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DOI

10.1016/0041-624x(79)90119-7

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ISSN

1432-1394

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Convex optimization under inequality constraints i

Authors: Lutz RoeseKoerner WolfDieter Schuh
Publish Date: 2014/01/24
Volume: 88, Issue: 5, Pages: 415-426
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Abstract

Many geodetic applications require the minimization of a convex objective function subject to some linear equality and/or inequality constraints If a system is singular eg a geodetic network without a defined datum this results in a manifold of solutions Most stateoftheart algorithms for inequality constrained optimization eg the ActiveSetMethod or primaldual InteriorPointMethods are either not able to deal with a rankdeficient objective function or yield only one of an infinite number of particular solutions In this contribution we develop a framework for the rigorous computation of a general solution of a rankdeficient problem with inequality constraints We aim for the computation of a unique particular solution which fulfills predefined optimality criteria as well as for an adequate representation of the homogeneous solution including the constraints Our theoretical findings are applied in a case study to determine optimal repetition numbers for a geodetic network to demonstrate the potential of the proposed frameworkThe authors would like to thank Professor Heiner Kuhlmann and the department of Geodesy in Bonn for providing the point coordinates of the network in the “Messdorfer Feld” and Maike Schumacher for establishing a SOD toolbox The comments of three anonymous reviewers are greatly acknowledged

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  11. Local Multiscale Modelling of Geoid Undulations from Deflections of the Vertical
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  13. Thermosteric Effects on Interannual and Long-term Global Mean Sea Level Changes
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  18. Bias in GRACE estimates of ice mass change due to accompanying sea-level change
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