Skip to main content
Erschienen in: Optimization and Engineering 2/2019

24.04.2019 | Editorial

Mixed-integer nonlinear programming 2018

verfasst von: Nikolaos V. Sahinidis

Erschienen in: Optimization and Engineering | Ausgabe 2/2019

Einloggen

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

search-config
loading …

Abstract

Mixed-Integer Nonlinear Programming (MINLP) is the area of optimization that addresses nonlinear problems with continuous and integer variables. MINLP has proven to be a powerful tool for modeling. At the same time, it combines algorithmic design challenges from combinatorial and nonlinear optimization. The MINLP field has received increased attention over the past two decades with contributions on the theoretical, algorithmic, and computational side originating from a growing community that involves engineers, mathematicians, and operations researchers. This special issue was motivated by a seminar on MINLP that took place in Dagstuhl, Germany in 2018. The purpose of this article is to provide a brief introduction to the field and the articles of the special issue.

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!

Literatur
Zurück zum Zitat Altherr LC, Leise P, Pfetsch ME, Schmitt A (2019) Resilient layout, design and operation of energy-efficient water distribution networks for high-rise buildings using MINLP. Optim Eng 20:605–645 Altherr LC, Leise P, Pfetsch ME, Schmitt A (2019) Resilient layout, design and operation of energy-efficient water distribution networks for high-rise buildings using MINLP. Optim Eng 20:605–645
Zurück zum Zitat Bazaraa MS, Sherali HD, Shetty CM (2006) Nonlinear programming, theory and algorithms, 3rd edn. Wiley, Hoboken, NJ Bazaraa MS, Sherali HD, Shetty CM (2006) Nonlinear programming, theory and algorithms, 3rd edn. Wiley, Hoboken, NJ
Zurück zum Zitat Belotti P, Lee J, Liberti L, Margot F, Wächter A (2009) Branching and bounds tightening techniques for non-convex MINLP. Optim Methods Softw 24:597–634MathSciNetCrossRefMATH Belotti P, Lee J, Liberti L, Margot F, Wächter A (2009) Branching and bounds tightening techniques for non-convex MINLP. Optim Methods Softw 24:597–634MathSciNetCrossRefMATH
Zurück zum Zitat Belotti P, Kirches Ch, Leyffer S, Linderoth J, Luedtke J, Mahajan A (2013) Mixed-integer nonlinear optimization. Acta Numer 22:1–131MathSciNetCrossRefMATH Belotti P, Kirches Ch, Leyffer S, Linderoth J, Luedtke J, Mahajan A (2013) Mixed-integer nonlinear optimization. Acta Numer 22:1–131MathSciNetCrossRefMATH
Zurück zum Zitat Blackburn L, Young A, Rogers P, Hedengren J, Powell K (2019) Dynamic optimization of a district energy system with storage using a novel mixed-integer quadratic programming algorithm. Optim Eng 20:575–603 Blackburn L, Young A, Rogers P, Hedengren J, Powell K (2019) Dynamic optimization of a district energy system with storage using a novel mixed-integer quadratic programming algorithm. Optim Eng 20:575–603
Zurück zum Zitat Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, CambridgeCrossRefMATH Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, CambridgeCrossRefMATH
Zurück zum Zitat Burlacu R, Egger H, Groß M, Martin A, Pfetsch ME, Schewe L, Sirvent M, Skutella M (2019) Maximizing the storage capacity of gas networks: a global MINLP approach. Optim Eng 20:543–573 Burlacu R, Egger H, Groß M, Martin A, Pfetsch ME, Schewe L, Sirvent M, Skutella M (2019) Maximizing the storage capacity of gas networks: a global MINLP approach. Optim Eng 20:543–573
Zurück zum Zitat Cay P, Mancilla C, Storer RH, Zuluaga LF (2019) Operational decisions for multi-period industrial gas pipeline networks under uncertainty. Optim Eng 20:647–682 Cay P, Mancilla C, Storer RH, Zuluaga LF (2019) Operational decisions for multi-period industrial gas pipeline networks under uncertainty. Optim Eng 20:647–682
Zurück zum Zitat D’Ambrosio C, Lee J, Liberti L, Ovsjanikov M (2019) Extrapolating curvature lines in rough concept sketches using mixed-integer nonlinear optimization. Optim Eng 20:337–347 D’Ambrosio C, Lee J, Liberti L, Ovsjanikov M (2019) Extrapolating curvature lines in rough concept sketches using mixed-integer nonlinear optimization. Optim Eng 20:337–347
Zurück zum Zitat Dantzig GB (1949) Programming in a linear structure. Econometrica 17:73–74CrossRef Dantzig GB (1949) Programming in a linear structure. Econometrica 17:73–74CrossRef
Zurück zum Zitat Dantzig GB (1963) Linear programming and extensions. Princeton University Press, PrincetonCrossRefMATH Dantzig GB (1963) Linear programming and extensions. Princeton University Press, PrincetonCrossRefMATH
Zurück zum Zitat Dantzig G, Fulkerson R, Johnson S (1954) Solution of a large-scale traveling-salesman problem. J Oper Res Soc Am 2:393–410MathSciNet Dantzig G, Fulkerson R, Johnson S (1954) Solution of a large-scale traveling-salesman problem. J Oper Res Soc Am 2:393–410MathSciNet
Zurück zum Zitat Dey SS, Santana A, Wang Y (2019) New SOCP relaxation and branching rule for bipartite bilinear programs. Optim Eng 20:307–336 Dey SS, Santana A, Wang Y (2019) New SOCP relaxation and branching rule for bipartite bilinear programs. Optim Eng 20:307–336
Zurück zum Zitat Duran MA, Grossmann IE (1986) An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Math Program 36:307–339MathSciNetCrossRefMATH Duran MA, Grossmann IE (1986) An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Math Program 36:307–339MathSciNetCrossRefMATH
Zurück zum Zitat Gleixner A, Bastubbe M, Eifler L, Gally T, Gamrath G, Gottwald RL, Hendel G, Hojny C, Koch Th, Lübbecke ME, Maher SJ, Miltenberger M, Müller B, Pfetsch ME, Puchert Ch, Rehfeldt D, Schlösser F, Schubert Ch, Serrano F, Shinano Y, Viernickel JM, Walter M, Wegscheider F, Witt JT, Witzig J (2018) The SCIP Optimization Suite 6.0, Technical Report, Optimization Online, July, 2018. Available at http://www.optimization-online.org/DB_HTML/2018/07/6692.html Gleixner A, Bastubbe M, Eifler L, Gally T, Gamrath G, Gottwald RL, Hendel G, Hojny C, Koch Th, Lübbecke ME, Maher SJ, Miltenberger M, Müller B, Pfetsch ME, Puchert Ch, Rehfeldt D, Schlösser F, Schubert Ch, Serrano F, Shinano Y, Viernickel JM, Walter M, Wegscheider F, Witt JT, Witzig J (2018) The SCIP Optimization Suite 6.0, Technical Report, Optimization Online, July, 2018. Available at http://​www.​optimization-online.​org/​DB_​HTML/​2018/​07/​6692.​html
Zurück zum Zitat González Rueda ÁM, González DJ, de Córdoba MPF (2019) A twist on SLP algorithms for NLP and MINLP problems: an application to gas transmission networks. Optim Eng 20:349–395 González Rueda ÁM, González DJ, de Córdoba MPF (2019) A twist on SLP algorithms for NLP and MINLP problems: an application to gas transmission networks. Optim Eng 20:349–395
Zurück zum Zitat Horst R, Tuy H (1996) Global optimization: deterministic approaches, 3rd edn. Springer, BerlinCrossRefMATH Horst R, Tuy H (1996) Global optimization: deterministic approaches, 3rd edn. Springer, BerlinCrossRefMATH
Zurück zum Zitat Khajavirad A, Sahinidis NV (2018) A hybrid LP/NLP paradigm for global optimization relaxations. Math Program Comput 10:383–421MathSciNetCrossRefMATH Khajavirad A, Sahinidis NV (2018) A hybrid LP/NLP paradigm for global optimization relaxations. Math Program Comput 10:383–421MathSciNetCrossRefMATH
Zurück zum Zitat Koster AMCA, Kuhnke S (2019) An adaptive discretization algorithm for the design of water usage and treatment networks. Optim Eng 20:497–542 Koster AMCA, Kuhnke S (2019) An adaptive discretization algorithm for the design of water usage and treatment networks. Optim Eng 20:497–542
Zurück zum Zitat Kronqvist J, Lundell A, Westerlund T (2016) The extended supporting hyperplane algorithm for convex mixed-integer nonlinear programming. J Glob Optim 64:249–272MathSciNetCrossRefMATH Kronqvist J, Lundell A, Westerlund T (2016) The extended supporting hyperplane algorithm for convex mixed-integer nonlinear programming. J Glob Optim 64:249–272MathSciNetCrossRefMATH
Zurück zum Zitat Kronqvist J, Bernal DE, Lundell A, Grossmann IE (2019) A review and comparison of solvers for convex MINLP. Optim Eng 20:397–455 Kronqvist J, Bernal DE, Lundell A, Grossmann IE (2019) A review and comparison of solvers for convex MINLP. Optim Eng 20:397–455
Zurück zum Zitat Kılınç M, Sahinidis NV (2017) State-of-the-art in mixed-integer nonlinear programming. In: Terlaky T, Anjos M, Ahmed S (eds) Advances and trends in optimization with engineering applications. MOS-SIAM book series on optimization. SIAM, Philadelphia, pp 273–292 Kılınç M, Sahinidis NV (2017) State-of-the-art in mixed-integer nonlinear programming. In: Terlaky T, Anjos M, Ahmed S (eds) Advances and trends in optimization with engineering applications. MOS-SIAM book series on optimization. SIAM, Philadelphia, pp 273–292
Zurück zum Zitat Kılınç M, Sahinidis NV (2019) Exploiting integrality in the global optimization of mixed-integer nonlinear programming problems in BARON. Optim Methods Softw 33:540–562MathSciNetMATH Kılınç M, Sahinidis NV (2019) Exploiting integrality in the global optimization of mixed-integer nonlinear programming problems in BARON. Optim Methods Softw 33:540–562MathSciNetMATH
Zurück zum Zitat Misener R, Floudas ChA (2014) ANTIGONE: algorithms for continuous/integer global optimization of nonlinear equations. J Glob Optim 59:503–526MathSciNetCrossRefMATH Misener R, Floudas ChA (2014) ANTIGONE: algorithms for continuous/integer global optimization of nonlinear equations. J Glob Optim 59:503–526MathSciNetCrossRefMATH
Zurück zum Zitat Nemhauser GL, Wolsey LA (1988) Integer and combinatorial optimization. Wiley interscience, series in discrete mathematics and optimization. Wiley, New York Nemhauser GL, Wolsey LA (1988) Integer and combinatorial optimization. Wiley interscience, series in discrete mathematics and optimization. Wiley, New York
Zurück zum Zitat Pecci F, Abraham E, Stoianov I (2019) Global optimality bounds for the placement of control valves in water supply networks. Optim Eng 20:457–495MATH Pecci F, Abraham E, Stoianov I (2019) Global optimality bounds for the placement of control valves in water supply networks. Optim Eng 20:457–495MATH
Zurück zum Zitat Trespalacios F, Grossmann IE (2014) Review of mixed-integer nonlinear and generalized disjunctive programming methods. Chem Ing Tech 86:991–1012CrossRef Trespalacios F, Grossmann IE (2014) Review of mixed-integer nonlinear and generalized disjunctive programming methods. Chem Ing Tech 86:991–1012CrossRef
Zurück zum Zitat Tuy H (1964) Concave programming under linear constraints. Dokl Akad Nauk 159:32–35MathSciNet Tuy H (1964) Concave programming under linear constraints. Dokl Akad Nauk 159:32–35MathSciNet
Metadaten
Titel
Mixed-integer nonlinear programming 2018
verfasst von
Nikolaos V. Sahinidis
Publikationsdatum
24.04.2019
Verlag
Springer US
Erschienen in
Optimization and Engineering / Ausgabe 2/2019
Print ISSN: 1389-4420
Elektronische ISSN: 1573-2924
DOI
https://doi.org/10.1007/s11081-019-09438-1

Weitere Artikel der Ausgabe 2/2019

Optimization and Engineering 2/2019 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.