Skip to main content
SpringerLink
Log in

Second Order Constraint Qualifications

  • Reference work entry
Encyclopedia of Optimization

  • 300 Accesses

Article Outline

Keywords

Remarks

See also

References

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

Access this chapter

Log in via an institution
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. Aubin J-P, Frankowska H (1990) Set-valued analysis. Birkhäuser, Basel

    MATH  Google Scholar 

  2. Ben-Tal A (1980) Second-order and related extremality conditions in nonlinear programming. J Optim Th Appl 31:143–165

    Article  MathSciNet  MATH  Google Scholar 

  3. Ben-Tal A, Zowe J (1982) A unified theory of first and second order conditions for extremum problems in topological vector spaces. Math Program Stud 19:39–76

    MathSciNet  Google Scholar 

  4. Bonnans JF, Cominetti R (1996) Perturbed optimization in Banach spaces I, II, III. SIAM J Control Optim 34:1151–1171; 1172–1189; 1555–1567

    Article  MathSciNet  MATH  Google Scholar 

  5. Bonnans JF, Cominetti R, Shapiro A (1998) Sensitivity analysis of optimization problems under abstract constraints. Math Oper Res 23:806–831

    Article  MathSciNet  MATH  Google Scholar 

  6. Bonnans JF, Cominetti R, Shapiro A (1999) Second order optimality conditions based on parabolic second order tangent sets. SIAM J Optim 9:466–492

    Article  MathSciNet  MATH  Google Scholar 

  7. Bonnans JF, Ioffe AD, Shapiro A (1992) Expansion of exact and approximate nonlinear programming. In: Oettli W, Pallaschke D (eds) Advances in Optimizations. Springer, Berlin, pp 103–117

    Google Scholar 

  8. Bonnans JF, Shapiro A (2000) Perturbation analysis of optimization problems. Springer, Berlin

    MATH  Google Scholar 

  9. Cominetti R (1990) Metric regularity, tangent sets and second-order optimality conditions. Appl Math Optim 21:265–287

    Article  MathSciNet  MATH  Google Scholar 

  10. Dien PH, Sach PH (1989) Second-order optimality conditions for the extremal problem under inclusion constraints. Appl Math Optim 20:71–80

    Article  MathSciNet  MATH  Google Scholar 

  11. Fiacco AV, McCormick GP (1968) Nonlinear programming: Sequential unconstrained minimization techniques. Wiley, New York

    MATH  Google Scholar 

  12. Hestenes MR (1975) Optimization theory – The finite-dimensional case. Wiley, New York

    MATH  Google Scholar 

  13. Hettich R, Jongen HTh (1978) Semi-infinite programming: conditions of optimality and applications. In: Stoer J (ed) Optimization Techniques 2. Springer, Berlin, pp 1–11

    Chapter  Google Scholar 

  14. Hettich R, Still G (1995) Second-order optimality conditions for generalized semi-infinite programming problems. Optim 34:195–211

    Article  MathSciNet  MATH  Google Scholar 

  15. Hiriart-Urruty J-B, Strodiot JJ, Nguyen V Hien (1984) Generalized Hessian matrix and second order optimality conditions for problems with C1,1-data. Appl Math Optim 11:43–56

    Article  MathSciNet  MATH  Google Scholar 

  16. Ioffe AD (1979) Necessary and sufficient conditions for a local minimum. 3: Second order conditions and augmmented duality. SIAM J Control Optim 17:266–288

    Article  MathSciNet  MATH  Google Scholar 

  17. Klatte D (1992) Stability of stationary solutions in semi-infinite optimization via the reduction approach. In: Oettli W, Pallaschke D (eds) Advances in Optimization. Springer, Berlin, pp 155–170

    Google Scholar 

  18. Levitin ES, Miljutin AA, Osmolovskii NP (1974) On conditions for a local minimum in a problem with constraints. In: Mitjagin BS (ed) Mathematical Economics and Functional Analysis. Nauka, Moscow, pp 139–202, in Russian

    Google Scholar 

  19. Luenberger DE (1973) Introduction to linear and nonlinear programming. Addison-Wesley, Reading

    MATH  Google Scholar 

  20. McCormick GP (1967) Second-order conditions for constrained minima. SIAM J Appl Math 15:641–652

    Article  MathSciNet  MATH  Google Scholar 

  21. Rockafellar RT, Wets RJ-B (1997) Variational analysis. Springer, Berlin

    Google Scholar 

  22. Shapiro A (1985) Second-order derivatives of extremal-value functions and optimality conditions for semi-infinite programs. Math Oper Res 10:207–219

    Article  MathSciNet  MATH  Google Scholar 

  23. Shapiro A (1997) First and second order analysis of nonlinear semidefinite programs. Math Program 77:301–320

    Google Scholar 

  24. Shapiro A (1998) First and second order optimality conditions and perturbation analysis of semi–infinite programming problems. In: Reemtsen R, Rückmann J-J (eds) Semi-Infinite Programming. Kluwer, Dordrecht, pp 103–133

    Google Scholar 

  25. Still G, Streng M (1996) Optimality conditions in smooth nonlinear programming. J Optim Th Appl 90:483–515

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute OR, University Zurich, Zurich, Switzerland

    Diethard Klatte

Authors
  1. Diethard Klatte
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Klatte, D. (2008). Second Order Constraint Qualifications . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_575

Download citation

Publish with us

Policies and ethics

Search

Navigation