Skip to main content
SpringerLink
Log in

Some Additional Informations on the Capacity of the Linear Complementarity Algorithm

  • Conference paper
Optimization and Design of Geodetic Networks

Summary

The development of analytical methods for optimization techniques within the whole spectrum of geodesy asks for algorithms, which are able to consider all the boundary constraints the solution has to fulfill. One of such algorithms is the linear complementarity algorithm described in some detail in the following. Practical applications complete theoretical insights for better understanding how to use the algorithm not only in optimization problems but also from a more general point of view coming from approximation theory.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Armstrong, R.D. (1980: A Linear Programming Algorithm for Curve Fitting in the L∞ Norm. Num. Funct. Anal, and Optimiz., 2: pp. 187–218.

    Article  Google Scholar 

  • Barrodale, I. (1968): L-l Approximations and the Analysis of Data. App. Statistics, 17: pp. 51–57.

    Article  Google Scholar 

  • Bazaraa, M.S./C.M. Shetty (1979): Nonlinear Programming. J. Wiley, New York.

    Google Scholar 

  • Bossler, J./E.W. Grafarend/R. Keim (1973): Optimal Design of Geodetic Nets 2 J. Geophys. Res., 78: pp. 5887–5897.

    Google Scholar 

  • Cottle, R.W./G.B. Dantzig (1968): Complementary Pivot Theory of Mathematical Programming. Lin.Alg.Appl., 1: pp. 103–125.

    Article  Google Scholar 

  • Cross, P.A./K. Thapa (1979): The Optimal Design of Levelling Networks. Survey Review, 25: pp. 68–79.

    Google Scholar 

  • Fritsch, D. (1982a): Second Order Design of Geodetic Networks - Problems and Examples. Deutsche Geod. Komm., Reihe B, Nr.258/III München.

    Google Scholar 

  • Fritsch, D. (1982b): Entwurf digitaler zweidimensionaler nichtrekursiver Filter. Deutsche Geod. Komm., Reihe C, Nr.275, München.

    Google Scholar 

  • Fuchs, H. (1982): Contributions to the Adjustment by Minimizing the Sum of Absolute Residuals. Manuscripta Geodaetica, 7 PP 151–207.

    Google Scholar 

  • Grafarend, E.W. (1974): Optimization of Geodetic Networks. Boll. Geod. Sci. Aff., 33: pp. 351–406.

    Google Scholar 

  • Grafarend, E.W. (1975): Second Order Desiqn of Geodetic Nets. Zeitschr. Verm. Wesen, 100: pp. 158–168.x

    Google Scholar 

  • Grafarend, E.W./B. Schaffrin/G. Schmitt (1976): Ãœber die Optimierung lokaler geodätischer Netze. Proc. VII. Int. Kurs Ing. Verm. hoher Präz., Vol.I, Darmstadt.

    Google Scholar 

  • Grimhardt, H./K. Schnädelbach (1983): Rigorous Adjustment of Horizontal Geodetic Networks with given Tolerance Intervals for the Observations. Pap. pres. to: IAG Gen. Ass., Hamburg.

    Google Scholar 

  • Koch, K.R. (1982): Optimization of the Configuration of Geodetic Networks. Deutsche Geod. Komm., Reihe B, Nr.258/III, München.

    Google Scholar 

  • Krabs, W. (1983): Einführung in die lineare und nichtlineare Optimierung für Ingenieure. Teubner, Stuttgart.

    Google Scholar 

  • Krarup, T./K. Kubik/J. Juhl (1980): Götterdämmerung over Least-Squares Adjustment. Proc. 14. Congr. ISPRS, Hamburg.

    Google Scholar 

  • Lemke, C.Z. (1968): On Complementary Pivot Theory. In: Mathematics of the Decision Sciences. Parti, Ed. G.B. Dantzig/A.F. Veinott,0020Am. Math. Soc., Providence.

    Google Scholar 

  • Liew, C.K. (1976): Inequality Constrained Least-Squares Estimation. JASA, 71 pp. 746–751.

    Google Scholar 

  • Liew, C.K./J.K. Shim (1978): A Computer Program for Inequality Constrained Least-Squares Estimation. Econometrica, 46: p. 237.

    Article  Google Scholar 

  • Milbert, D.G. (1979): Optimization of Horizontal Control Networks by Nonlinear Programming. NOAA Techn. Rep. NOS 79 NGS 12, Rockville.

    Google Scholar 

  • Proll, L.G. (1974) Remark on Algorithm 431. Com. ACM, 17: pp. 590.

    Article  Google Scholar 

  • Ralston, A. (1965): A First Course in Numerical Analysis. Mc Graw-Hill, New York.

    Google Scholar 

  • Ravindran, A. (1972): Algrithm 431: A Computer Routine for Quadratic and Linear Programming Problems. Com. ACM, 15: pp. 818–820.

    Google Scholar 

  • Schaffrin, B./E.W. Grafarend/G. Schmitt (1977): Kanonisches Design Geodätischer Netze I. Manuscripta Geodaetica, 2: S. 263–306.

    Google Scholar 

  • Schaffrin, B. (1978): Personal communications.

    Google Scholar 

  • Schaffrin, B. (1981a): Some Proposals Concerning the Diagonal Second Order. Design of Geodetic Networks. Manuscripta Geodaetica, 6: pp. 303–326.

    Google Scholar 

  • Schaffrin, B. (1981b): Ausgleichung mit Bedinqunqs-Ungleichungen. Allaem.Verm. Nachr., 6: S. 227–238.

    Google Scholar 

  • Schaffrin, B./F. Krumm/D. Fritsch (1982): Positiv - diagonale Genauigkeitsoptimierung von Real netzen Ãœber den Komplementaritäts - Alqorithmus. In: Ingenieurvermessung 80. Ed.R. Conzett/H.J. Matthias/H. Schmid.

    Google Scholar 

  • Schmitt, G./E.W. Grafarend/B. Schaffrin (1978): Kanonisches Desiqn Geodätischer Netze II. Manuscripta Geodaetica, 3: S. 1–22.

    Google Scholar 

  • Schreiber, O. (1882): Anordnung der Winkelbeobachtungen im Göttinger Basisnetz. Zeitschr. Verm. Wesen, 11: S. 129 ff.

    Google Scholar 

  • Schreiber, O. (1889): Ãœber die günstigste Gewichtsverteilung. Zeitschr. Verm. Wesen, 18: S. 57 ff.

    Google Scholar 

  • Stummel, F./K. Hainer (1982): Praktische Mathematik. Teubner, Stuttgart.

    Google Scholar 

Download references

Authors
  1. D. Fritsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Geodätisches Institut, Universität Stuttgart, Keplerstraße 11, 7000, Stuttgart 1, Germany

    Erik W. Grafarend

  2. Fotogrammetria e Geofisica, Istituto di Topografia, Piazza Leonardo da Vinci, 32, 20133, Milano, Italy

    Fernando Sansò

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fritsch, D. (1985). Some Additional Informations on the Capacity of the Linear Complementarity Algorithm. In: Grafarend, E.W., Sansò, F. (eds) Optimization and Design of Geodetic Networks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-70659-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-70659-2_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-70661-5

  • Online ISBN: 978-3-642-70659-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation