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

2012 | OriginalPaper | Chapter

2. Polynomial Optimization Over the Euclidean Ball

Authors : Zhening Li, Simai He, Shuzhong Zhang

Published in: Approximation Methods for Polynomial Optimization

Publisher: Springer New York

Log in

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

search-config
loading …

Abstract

In this chapter, we shall present approximation methods for polynomial optimization. The focus will be placed on optimizing several classes of polynomial functions over the Euclidean ball.

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 Introduction
next chapter Extensions of the Constraint Sets
Literature
24.
48.
He, S., Luo, Z.-Q., Nie, J., Zhang, S.: Semidefinite relaxation bounds for indefinite homogeneous quadratic optimization. SIAM J. Optim. 19, 503–523 (2008)MathSciNetMATHCrossRef
65.
66.
72.
Ling, C., Nie, J., Qi, L., Ye, Y.: Biquadratic optimization over unit spheres and semidefinite programming relaxations. SIAM J. Optim. 20, 1286–1310 (2009)MathSciNetMATHCrossRef
74.
Luo, Z.-Q., Sidiropoulos, N.D., Tseng, P., Zhang, S.: Approximation bounds for quadratic optimization with homogeneous quadratic constraints. SIAM J. Optim. 18, 1–28 (2007)MathSciNetMATHCrossRef
76.
Luo, Z.-Q., Zhang, S.: A semidefinite relaxation scheme for multivariate quartic polynomial optimization with quadratic constraints. SIAM J. Optim. 20, 1716–1736 (2010)MathSciNetMATHCrossRef
82.
86.
Nemirovski, A., Roos, C., Terlaky, T.: On maximization of quadratic form over intersection of ellipsoids with common center. Math. Progr. Ser. A 86, 463–473 (1999)MathSciNetMATHCrossRef
87.
89.
Nesterov, Yu.: Random walk in a simplex and quadratic optimization over convex polytopes, CORE Discussion Paper 2003/71. Université catholique de Louvain, Louvain-la-Neuve (2003)
99.
Qi, L.: Eigenvalues of a real supersymmetric tensor. J. Symb. Comput. 40, 1302–1324 (2005)MATHCrossRef
106.
So, A.M.-C.: Deterministic approximation algorithms for sphere constrained homogeneous polynomial optimization problems. Math. Progr. Ser. B 129, 357–382 (2011)MathSciNetMATHCrossRef
110.
111.
Sun, W., Yuan, Y.-X.: Optimization Theory and Methods: Nonlinear Programming. Springer, New York (2006)MATH
113.
Varjú, P.P.: Approximation by homogeneous polynomials. Construct. Approx. 26, 317–337 (2007)MATH
117.
Zhang, S.: Quadratic maximization and semidefinite relaxation. Math. Progr. Ser. A 87, 453–465 (2000)MATHCrossRef
Metadata
Title
Polynomial Optimization Over the Euclidean Ball
Authors
Zhening Li
Simai He
Shuzhong Zhang
Copyright Year
2012
Publisher
Springer New York
Book
Approximation Methods for Polynomial Optimization

Print ISBN: 978-1-4614-3983-7

Electronic ISBN: 978-1-4614-3984-4

Copyright Year: 2012

DOI
https://doi.org/10.1007/978-1-4614-3984-4_2