Roese-Koerner, Lutz Rolf: Convex optimization for inequality constrained adjustment problems. - Bonn, 2015. - , . In: Schriftenreihe / Institut für Geodäsie und Geoinformation, 50.
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author = {{Lutz Rolf Roese-Koerner}},
title = {Convex optimization for inequality constrained adjustment problems},
school = {},
year = 2015,
series = {Schriftenreihe / Institut für Geodäsie und Geoinformation},
volume = 50,
note = {Whenever a certain function shall be minimized (e.g., a sum of squared residuals) or maximized (e.g., profit) optimization methods are applied. If in addition prior knowledge about some of the parameters can be expressed as bounds (e.g., a non-negativity bound for a density) we are dealing with an optimization problem with inequality constraints. Although, common in many economic and engineering disciplines, inequality constrained adjustment methods are rarely used in geodesy. Within this thesis methodology aspects of convex optimization methods are covered and analogies to adjustment theory are provided. Furthermore, three shortcomings are identified which are - in the opinion of the author - the main obstacles that prevent a broader use of inequality constrained adjustment theory in geodesy. First, most optimization algorithms do not provide quality information of the estimate. Second, most of the existing algorithms for the adjustment of rank-deficient systems either provide only one arbitrary particular solution or compute only an approximative solution. Third, the Gauss-Helmert model with inequality constraints was hardly treated in the literature so far. We propose solutions for all three obstacles and provide simulation studies to illustrate our approach and to show its potential for the geodetic community. Thus, the aim of this thesis is to make accessible the powerful theory of convex optimization with inequality constraints for classic geodetic tasks.},
url = {}

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