Advertisement

Optimization Letters

, Volume 1, Issue 2, pp 187–192 | Cite as

On the functional form of convex underestimators for twice continuously differentiable functions

  • Christodoulos A. Floudas
  • Vladik Kreinovich
Original Paper

Abstract

The optimal functional form of convex underestimators for general twice continuously differentiable functions is of major importance in deterministic global optimization. In this paper, we provide new theoretical results that address the classes of optimal functional forms for the convex underestimators. These are derived based on the properties of shift-invariance and sign- invariance.

Keywords

Global Optimization Differentiable Function Global Optimization Method MINLP Problem Deterministic Global Optimization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adjiman C.S., Floudas C.A.(1996): Rigorous convex underestimators for general tweice-differentiable problems. J. Global Optim. 9, 23–40zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Adjiman C.S., Dallwig S., Androulakis I., Floudas C.A., Neumaier A.(1998): A global optimization method, αBB, for general twice-differentiable constrained NLP I. Theoretical aspects. Comput. Chem. Eng. 22(9): 1137–1158Google Scholar
  3. 3.
    Adjiman C.S., Androulakis I., Floudas C.A.(1998): A global optimization method, αBB, for general twice-differentiable constrained NLP II Implementation and computational results. Comput. Chem. Eng. 22, 1159–1179CrossRefGoogle Scholar
  4. 4.
    Akrotirianakis I.G., Floudas C.A.(2004): Computational experience with a new class of convex underestimators: box-constrained NLP problems. J. Global Optim., 29, 249–264zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Akrotirianakis I.G., Floudas C.A.(2004): A new class of improved convex underestimators for twice continuously differentiable constrained NLPs. J. Global Optim. 30, 367–390zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Androulakis I.P., Maranas C.D., Floudas C.A. (1995): Alpha BB: a global optimization method for general constrained nonconvex problems. J. Global Optim. 7, 337–363zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Floudas C.A.(2000): Deterministic Global Optimization: Theory, Methods, and Applications. Kluwer, DordrechtGoogle Scholar
  8. 8.
    Floudas C.A.(2005): Research challenges, opportunities and synergism in systems engineering and computational biology. AIChE J. 51, 1872–1884CrossRefGoogle Scholar
  9. 9.
    Floudas, C.A., Kreinovich, V.: Towards optimal techniques for solving global optimization problems: symmetry-based approach. In. Torn, A., Zilinskas, J. (eds.) Models, and Algorithms for Global Optimization, Springer, Dordrecht (to appear) (2006)Google Scholar
  10. 10.
    Floudas C.A., Akrotirianakis I.G., Caratzoulas S., Meyer C.A., Kallrath J. (1995): Global optimization in the 21st century: advances and challenges. Comput. Chem. Eng. 29, 1185–1202CrossRefGoogle Scholar
  11. 11.
    Maranas C.D., Floudas C.A.(1994): Global minimal potential energy conformations for small molecules. J. Global Optim. 4, 135–170zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Adjiman C.S., Androulakis I.P., Maranas C.D., Floudas C.A. (1996): A global optimization method, alphaBB, for process design. Comput. Chem. Eng. 20, S419–S424CrossRefGoogle Scholar
  13. 13.
    Maranas C.D., Floudas C.A.(1995): Finding all solutions of nonlinearly constrained systems of equations. J. Global Optim. 7(2): 143–182zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Androulakis I.P., Maranas C.D., Floudas C.A.(1997): Prediction of oligopeptide conformations via deterministic global optimization. J. Global Optim. 11(1): 1–34zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Adjiman C.S., Androulkis I.P., Floudas C.A.(1997): Global optimization of MINLP problems in process synthesis and design. Comput. Chem. Eng. 21, S445–S450Google Scholar
  16. 16.
    Adjiman C.S., Androulakis I.P., Floudas C.A. (2000): Global optimization of mixed-integer nonlinear problems. AIChE J. 46(9): 1769–1797CrossRefGoogle Scholar
  17. 17.
    Esposito W.R., Floudas C.A.(1998): Global optimization in parameter estimation of nonlinear algebraic models via the error-in-variables approach. Ind. Eng. Chem. Res. 37(5): 1841–1858CrossRefGoogle Scholar
  18. 18.
    Esposito W.R., Floudas C.A. (2000): Global optimization in parameter estimation of differential-algebraic systems. Ind. Eng. Chem. Res. 39(5): 1291–1310CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Chemical EngineeringPrinceton UniversityPrincetonUSA
  2. 2.Department of Computer ScienceUniversity of Texas at El PasoEl PasoUSA

Personalised recommendations