Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Introduction Read chapter Read first chapter

2021 | OriginalPaper | Chapter

11. Applications and Numerical Results

Author : Roman A. Polyak

Published in: Introduction to Continuous Optimization

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this chapter we describe several real-life applications and provide results obtained by solving truss topology design (TTD), intensity-modulated radiation therapy planning, support vector machine, non-negative least squares, and economic equilibrium. We also provide numerical results of testing both nonlinear and linear optimization problems. The results obtained strongly corroborate the theory.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now

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!

inform now
previous chapter Finding Nonlinear Equilibrium
Literature
Alber, M., Reemtsen, R.: Intensity modulated radiotherapy treatment planning by use of a barrier-penalty multiplier method. Optim. Methods Software 22(3), 391–411 (2007)MathSciNetCrossRef
Bailey, D., Townsend, D., Valk, P., Maisey, M.: Positron Emmission Tomography. In: Basic Sciences Secaucus. Springer, London (2005)
Ben-Tal, A., Nemirovski, A.: Optimal design of engineering structures. In: Optima, vol. 47 (1995)
Ben-Tal, A., Nemirovski, A.: Lectures on Modern Convex Optimization Analysis, Algorithms and Engineering Applications. SIAM, Philadelphia (2001)
Ben-Tal, A., Yuzefovich, B., Zibulevsky, M.: Penalty-Barrier Multipliers Method for Minimax and Constrained Smooth Convex Optimization. Technion, Research report, pp. 9–92 (1992)
Benthem, M., Keenan, M.: Fast algorithm for the solution of large-scale non-negativity constrained least squares problems, J. Chemom. 18, 441–450 (2004)CrossRef
Berke, L., Khot, N., Polyak, R., Schneur, R.: Structural optimization using Newton modified barrier method. Struct. Optim. 10(3), 209–216 (1995)MATH
Breitfeld, M., Shanno, D.: Computational experience with modified log-barrier methods for nonlinear programming. Annals Oper. Res. 62, 439–464 (1996)MathSciNetCrossRef
Griva, I., Polyak, R.: Primal-dual nonlinear rescaling method with dynamic scaling parameter update. Math. Program. Ser. A 106, 237–259 (2006)MathSciNetCrossRef
Griva, I., Polyak, R.: 1.5-Q- superlinear convergence of an exterior point method for constrained optimization. J. Global Optim. 40, 679–695 (2008)
Griva, I., Polyak, R., Sobieski, J.: The Newton log-sigmoid method in constrained optimization, a collection of technical papers. In: Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, vol. 3, pp. 2193–2201 (1998)
Griva, I., Polyak, R., Shen-Shyang, H.: Support vector machine via nonlinear rescaling method. Optim. Lett. 1, 367–378 (2007)MathSciNetCrossRef
Gusev, M., Evans, D.: The fastest matrix vector multiplication. Parallel Algorithms Appl. 1(1), 57–67 (1993)CrossRef
Jarre, F., Kocvara, M., Zowe, J.: Interior point methods for mechanical design problems. Preprint No. 173, Institut fur Angewandte Matematik, Universitat Erlangen Nurnber, Martensstr. 3, D-91058 Erlangen, Germany (1996)
Jensen, D., Polyak, R., Schneur, R.: Experience with Modified Barrier Function Methods for Linear Programming, Research Report Department of Mathematical Sciences, vol. 10598. IBM T.J. Watson Research Center, New York, pp. 1–35 (1993)
Kočvara, M., Stingl, M.: Resent Progress in the NLP-SDP Code PENNON, Workshop “Optimization and Applications”, Oberwalfach (2005)
Kočvara, M., Stingl, M.: On the solution of large-scale SDP problems by the modified barrier method using iterative solvers. Math. Program. Series B 109(2–3), 413–444 (2007)MathSciNetCrossRef
Kočvara, M., Stingl, M.: PENNON: Software for Linear and Nonlinear Matrix Inequalities (2015). arXiv:1504.07212v2 [mat. OC]
Lawson, C., Hanson, R.: Solving Least Squares Problems. In: SIAM Classic in Apply Mathematics, Philadelphia (1995)
Migdalas, A., Pardalos, P., Storoy, S.: Parallel Computing in Optimization. Kluwer Academic Publishers, Dordrecht (1997)CrossRef
Nash, S., Polyak, R., Sofer, A.: A numerical comparison of barrier and modified – barrier methods for large–scale bound–constrained optimization. In: Large scale Optimization: State of Art. Kluwer Academic, Dordrecht (1994)
Polyak, R.: The projected gradient method for non-negative least squares. In: Contemporary Mathematics, vol. 636. AMS, New York, pp. 167–179 (2015)
Polyak, R., Costa, J., Neyshabouri, S.: Dual fast projected gradient method for quadratic programming. Optim. Lett. 7(4), 631–645 (2013)MathSciNetCrossRef
Quinn, M.: Parallel programming in C with MPI and Open MP. McGraw-Hill, New York (2004)
Shepp, L., Vardi, Y.: Maximin likelihood reconstruction in emission tomography. IEEE Trans. Med. Imaging 1(2), 113–122 (1982)CrossRef
Vapnik, V.: Statistical Learning Theory, Wiley, New York (1998)MATH
Vapnik, V.: The Nature of Statistical Learning Theory, 2nd edn. Springer, Berlin (2000)CrossRef
Metadata
Title
Applications and Numerical Results
Author
Roman A. Polyak
Copyright Year
2021
Book
Introduction to Continuous Optimization

Print ISBN: 978-3-030-68711-3

Electronic ISBN: 978-3-030-68713-7

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-68713-7_11

Premium Partner

    Image Credits