Skip to main content

Global Optimization: Functional Forms

  • Reference work entry
Encyclopedia of Optimization

Article Outline

Keywords and Phrases

Introduction

Selecting Convex Underestimators: The αBB Method

  Shift Invariance

  Sign Invariance

  Scale Invariance

  Generalization of Shift Invariance

Final Remarks

References

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 2,500.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 2,499.99
Price excludes VAT (USA)
  • Durable hardcover 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

References

  1. Adjiman CS, Androulakis IP, Floudas CA (1998) A Global Optimization Method, αBB, for General Twice-Differentiable Constrained NLPs II. Implementation and Computational Results. Comput Chem Eng 22:1159–1179

    Article  Google Scholar 

  2. Adjiman CS, Dallwig S, Floudas CA, and Neumaier A (1998) A Global Optimization Method, αBB, for General Twice-Differentiable Constrained NLPs I. Theoretical Advances. Comput Chem Eng 22:1137–1158

    Article  Google Scholar 

  3. Adjiman CS, Floudas CA (1996) Rigorous Convex Underestimators for General Twice-Differentiable Problems. J Global Optim 9:23–40

    Article  MathSciNet  MATH  Google Scholar 

  4. Akrotirianakis IG, Floudas CA (2004) A New Class of Improved Convex Underestimators for Twice Continuously Differentiable Constrained NLPs. J Global Optim 30:367–390

    Article  MathSciNet  MATH  Google Scholar 

  5. Akrotirianakis IG, Floudas CA (2004) Computational Experience with a New Class of Convex Underestimators : Box-Constrained NLP Problems. J Global Optim 29:249–264

    Article  MathSciNet  MATH  Google Scholar 

  6. Androulakis IP, Maranas CD, Floudas CA (1995) αBB: A Global Optimization Method for General Constrained Nonconvex Problems. J Global Optim 7:337–363

    Article  MathSciNet  MATH  Google Scholar 

  7. Floudas CA (2000) Deterministic Global Optimization: Theory, Algorithms and Applications. Kluwer, Dordrecht

    Google Scholar 

  8. Floudas CA, Akrotirianakis IG, Caratzoulas S, Meyer CA, Kallrath J (2005) Global Optimization in the 21st Century: Advances and Challenges. Comput Chem Eng 29:1185–1202

    Article  Google Scholar 

  9. Floudas CA, Kreinovich V (2006) Towards Optimal Techniques for Solving Global Optimization Problems: Symmetry-Based Approach. In: Torn A, Zilinskas J (eds) Models and Algorithms for Global Optimization. Springer, Berlin, pp 21–42

    Google Scholar 

  10. Floudas CA, Kreinovich V (2007) On the Functional Form of Convex Understimators for Twice Continuously Differentiable Functions. Optim Lett 1:187–192

    Article  MathSciNet  MATH  Google Scholar 

  11. Hertz D, Adjiman CS, Floudas CA (1999) Two results on bounding the roots of interval polynomials. Comput Chem Eng 23:1333–1339

    Article  Google Scholar 

  12. Iourinski D, Starks SA, Kreinovich V, Smith SF (2002) Swarm Intelligence: Theoretical Proof that Empirical Techniques are Optimal. In: Proceedings of the 2002 World Automation Congress WAC 2002, Orlando, FL, pp 107–112

    Google Scholar 

  13. Kearfott RB, Kreinovich V (2005) Beyond Convex? Global Optimization is Feasible only for Convex Objective Functions: A Theorem. J Global Optim 33:617–624

    Article  MathSciNet  MATH  Google Scholar 

  14. Kennedy J, Eberhart R, Shi Y (2001) Swarm Intelligence. Morgan Kaufmann, New York

    Google Scholar 

  15. Kreinovich V, Starks SA, Meyer G (1997) On a Theoretical Justification of the Choice of Epsilon-Inflation in PASCAL-XSC. Reliable Comput 3:437–452

    Article  MATH  Google Scholar 

  16. Maranas CD, Floudas CA (1994) Global Minimum Potential Energy Conformations of Small Molecules. J Global Optim 4:135–170

    Article  MathSciNet  MATH  Google Scholar 

  17. Nguyen HT, Kreinovich V (1997) Applications of Continuous Mathematics to Computer Science. Kluwer, Dordrecht

    MATH  Google Scholar 

  18. Rump SM (1998) A Note on Epsilon-Inflation. Reliable Comput 4:371–375

    Article  MathSciNet  MATH  Google Scholar 

  19. Vavasis SA (1991) Nonlinear Optimization: Complexity Issues. Oxford University Press, Oxford

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Gounaris, C.E., Floudas, C.A. (2008). Global Optimization: Functional Forms . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_232

Download citation

Publish with us

Policies and ethics