Skip to main content

2017 | OriginalPaper | Buchkapitel

9. Linearly Constrained Augmented Lagrangian: MINOS

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this chapter we present one of the most respectable algorithms and softwares for solving general nonlinear optimization problems given by Murtagh and Saunders (1978, 1980, 1982, 1995). The main idea behind this method is to generate a step by minimizing the Lagrangian or the augmented Lagrangian subject to the linearizations of the constraints.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Andrei, N. (2011a) Critica raţiunii algoritmilor de programare liniară. [Criticism of the Linear Programming Algorithms Reasoning]. Editura Academiei Române, Bucureşti. Andrei, N. (2011a) Critica raţiunii algoritmilor de programare liniară. [Criticism of the Linear Programming Algorithms Reasoning]. Editura Academiei Române, Bucureşti.
Zurück zum Zitat Arrow, K. J., & Sollow, R. M. (1958). Gradient methods for constrained maxima, with weakened assumptions. In K. J. Arrow, L. Hurwicz, & H. Uzawa (Eds.), Studies in linear and nonlinear programming (pp. 166–176). Stanford, CA, USA: Stanford University Press. Arrow, K. J., & Sollow, R. M. (1958). Gradient methods for constrained maxima, with weakened assumptions. In K. J. Arrow, L. Hurwicz, & H. Uzawa (Eds.), Studies in linear and nonlinear programming (pp. 166–176). Stanford, CA, USA: Stanford University Press.
Zurück zum Zitat Carolan, W. J., Hill, J. E., Kennington, J. L., Niemi, S., & Wochmann, S. J. (1990). An empirical evaluation of the KORBX algorithms for military airlift applications. Operations Research, 38, 240–248.CrossRef Carolan, W. J., Hill, J. E., Kennington, J. L., Niemi, S., & Wochmann, S. J. (1990). An empirical evaluation of the KORBX algorithms for military airlift applications. Operations Research, 38, 240–248.CrossRef
Zurück zum Zitat Dantzig, G. B. (1963). Linear programming and extensions. Princeton, NJ, USA: Princeton University Press.CrossRefMATH Dantzig, G. B. (1963). Linear programming and extensions. Princeton, NJ, USA: Princeton University Press.CrossRefMATH
Zurück zum Zitat GAMS – The solver manuals. (2005). GAMS Development Corporation. GAMS – The solver manuals. (2005). GAMS Development Corporation.
Zurück zum Zitat Gay, D. M. (1985). Electronic mail distribution of linear programming test problems. Mathematical Programming Society COAL Newsletter. Gay, D. M. (1985). Electronic mail distribution of linear programming test problems. Mathematical Programming Society COAL Newsletter.
Zurück zum Zitat Gill, P. E., & Murray, W. (1974a). Methods for large-scale linearly constrained problems. In P. E. Gill & W. Murray (Eds.), Numerical methods for constrained optimization (pp. 93–147). London\New York\San Francisco: Academic. Gill, P. E., & Murray, W. (1974a). Methods for large-scale linearly constrained problems. In P. E. Gill & W. Murray (Eds.), Numerical methods for constrained optimization (pp. 93–147). London\New York\San Francisco: Academic.
Zurück zum Zitat Gill, P. E., Murray, W., Saunders, M. A., & Wright, M. H. (1987). Maintaining LU factors of a general sparse matrix. Linear Algebra and its Applications, 88/89, 239–270.MathSciNetCrossRefMATH Gill, P. E., Murray, W., Saunders, M. A., & Wright, M. H. (1987). Maintaining LU factors of a general sparse matrix. Linear Algebra and its Applications, 88/89, 239–270.MathSciNetCrossRefMATH
Zurück zum Zitat Hellerman, E., & Rarick, D. (1971). Reinversion with the preassigned pivot procedure. Mathematical Programming, 1, 195–216.MathSciNetCrossRefMATH Hellerman, E., & Rarick, D. (1971). Reinversion with the preassigned pivot procedure. Mathematical Programming, 1, 195–216.MathSciNetCrossRefMATH
Zurück zum Zitat Hellerman, E., & Rarick, D. (1972). The partitioned preassigned pivot procedure (P4). In D. J. Rose & R. A. Willoughby (Eds.), Sparse Matrices and their Applications (pp. 67–76). New York, NY, USA: Plenum Press.CrossRef Hellerman, E., & Rarick, D. (1972). The partitioned preassigned pivot procedure (P4). In D. J. Rose & R. A. Willoughby (Eds.), Sparse Matrices and their Applications (pp. 67–76). New York, NY, USA: Plenum Press.CrossRef
Zurück zum Zitat Hestens, M. R. (1969). Multiplier and gradient methods. Journal of Optimization Theory and Applications, 4, 303–320.MathSciNetCrossRef Hestens, M. R. (1969). Multiplier and gradient methods. Journal of Optimization Theory and Applications, 4, 303–320.MathSciNetCrossRef
Zurück zum Zitat Murtagh, B. A., & Saunders, M. A. (1978). Large-scale linearly constrained optimization. Mathematical Programming, 14, 41–72.MathSciNetCrossRefMATH Murtagh, B. A., & Saunders, M. A. (1978). Large-scale linearly constrained optimization. Mathematical Programming, 14, 41–72.MathSciNetCrossRefMATH
Zurück zum Zitat Murtagh, B. A., & Saunders, M. A. (1980). MINOS/AUGMENTED user’s manual. (Technical Report SOL 80–14, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, California, CA 94305). Murtagh, B. A., & Saunders, M. A. (1980). MINOS/AUGMENTED user’s manual. (Technical Report SOL 80–14, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, California, CA 94305).
Zurück zum Zitat Murtagh, B. A., & Saunders, M. A. (1982). A projected lagrangian algorithm and its implementation for sparse nonlinear constraints. Mathematical Programming Study, 16, 84–117.MathSciNetCrossRefMATH Murtagh, B. A., & Saunders, M. A. (1982). A projected lagrangian algorithm and its implementation for sparse nonlinear constraints. Mathematical Programming Study, 16, 84–117.MathSciNetCrossRefMATH
Zurück zum Zitat Murtagh, B. A., & Saunders, M. A. (1995). MINOS 5.4 user’s guide. (Technical Report SOL 83-20R, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, California, CA 94305, February 1995). Murtagh, B. A., & Saunders, M. A. (1995). MINOS 5.4 user’s guide. (Technical Report SOL 83-20R, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, California, CA 94305, February 1995).
Zurück zum Zitat Nocedal, J., & Wright, S. J. (2006). Numerical optimization, Springer series in operations research (2nd ed.). New York, NY, USA: Springer Science+Business Media.MATH Nocedal, J., & Wright, S. J. (2006). Numerical optimization, Springer series in operations research (2nd ed.). New York, NY, USA: Springer Science+Business Media.MATH
Zurück zum Zitat Powell, M. J. D. (1969). A method for nonlinear constraints in optimization problems. In R. Fletcher (Ed.), Optimization (pp. 283–297). New York, NY, USA: Academic. Powell, M. J. D. (1969). A method for nonlinear constraints in optimization problems. In R. Fletcher (Ed.), Optimization (pp. 283–297). New York, NY, USA: Academic.
Zurück zum Zitat Robinson, S. M. (1972). A quadratically convergent algorithm for general nonlinear programming problems. Mathematical Programming, 3, 145–156.MathSciNetCrossRefMATH Robinson, S. M. (1972). A quadratically convergent algorithm for general nonlinear programming problems. Mathematical Programming, 3, 145–156.MathSciNetCrossRefMATH
Zurück zum Zitat Rosen, J. B., & Kreuser, J. (1972). A gradient projection algorithm for nonlinear constraints. In F. Lootsma (Ed.), Numerical methods for nonlinear optimization (pp. 297–300). London, UK: Academic. Rosen, J. B., & Kreuser, J. (1972). A gradient projection algorithm for nonlinear constraints. In F. Lootsma (Ed.), Numerical methods for nonlinear optimization (pp. 297–300). London, UK: Academic.
Zurück zum Zitat Saunders, M. (2015a). LUSOL – a basis factorization package. (Notes 6. Stanford University, Management Science & Engineering. Spring 2015). Saunders, M. (2015a). LUSOL – a basis factorization package. (Notes 6. Stanford University, Management Science & Engineering. Spring 2015).
Zurück zum Zitat Saunders, M. (2015b) Augmented Lagrangian methods. (Notes 9. Stanford University, Management Science & Engineering. Spring 2015). Saunders, M. (2015b) Augmented Lagrangian methods. (Notes 9. Stanford University, Management Science & Engineering. Spring 2015).
Zurück zum Zitat Vanderbei, R. J. (2001). Linear programming: Foundations and extensions (2nd ed.). New York, NY, USA: Springer.CrossRefMATH Vanderbei, R. J. (2001). Linear programming: Foundations and extensions (2nd ed.). New York, NY, USA: Springer.CrossRefMATH
Zurück zum Zitat Wolfe, P. (1967). Methods of nonlinear programming. In J. Abadie (Ed.), Nonlinear programming (pp. 97–131). Amsterdam, Europe: North-Holland. Wolfe, P. (1967). Methods of nonlinear programming. In J. Abadie (Ed.), Nonlinear programming (pp. 97–131). Amsterdam, Europe: North-Holland.
Zurück zum Zitat Wright, M. H. (1976). Numerical methods for nonlinearly constrained optimization. (SLAC Report No.193, 1976, Stanford University, California, 1976. (Ph.D. Dissertation)). Wright, M. H. (1976). Numerical methods for nonlinearly constrained optimization. (SLAC Report No.193, 1976, Stanford University, California, 1976. (Ph.D. Dissertation)).
Metadaten
Titel
Linearly Constrained Augmented Lagrangian: MINOS
verfasst von
Neculai Andrei
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-58356-3_9