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Duality for Semidefinite Programming

  • Reference work entry
Encyclopedia of Optimization

Article Outline

Keywords

Synonyms

Basic Properties

Strong Duality

Strict Complementarity

Closing the Duality Gap

Extensions

See also

References

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References

  1. Alfakih A, Khandani A, Wolkowicz H (1997) Solving Euclidean distance matrix completion problems via semidefinite programming. Techn Report CORR Univ Waterloo 98-9, in Computational Optim and Appl

    Google Scholar 

  2. Borwein JM, Wolkowicz H (1981) Characterizations of optimality for the abstract convex program with finite dimensional range. J Austral Math Soc (Ser A) 30:390–411

    MATH  MathSciNet  Google Scholar 

  3. Borwein JM, Wolkowicz H (1981) Regularizing the abstract convex program. J Math Anal Appl 83:495–530

    Article  MATH  MathSciNet  Google Scholar 

  4. Goldman AJ, Tucker AW (1956) Polyhedral convex cones. Linear equalities and related systems. In: Ann of Math Stud, vol 38. Princeton Univ. Press, Princeton, pp 19–40

    Google Scholar 

  5. Goldman AJ, Tucker AW (1956) Theory of linear programming. Linear inequalities and related systems. In: Ann of math Stud, vol 38. Princeton Univ. Press, Princeton, pp 53–97

    Google Scholar 

  6. Johnson CR, Kroschel B, Wolkowicz H (1998) An interior-point method for approximate positive semidefinite completions. Comput Optim Appl 9(2):175–190

    Article  MATH  MathSciNet  Google Scholar 

  7. Klerk Ede (1997) Interior point methods for semidefinite programming. PhD Thesis Delft Univ

    Google Scholar 

  8. Pataki G, Tuncel L (1997) On the generic properties of convex optimization problems in conic form. Techn Report CORR Dept Combinatorics and Optim Waterloo, Ont 97-16

    Google Scholar 

  9. Ramana MV (1993) An algorithmic analysis of multiquadratic and semidefinite programming problems. PhD Thesis Johns Hopkins Univ, Baltimore, Md

    Google Scholar 

  10. Ramana M, Tuncel L, Wolkowicz H (1997) Strong duality for semidefinite programming. SIAM J Optim 7(3):641–662

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  12. Wolkowicz H (1981) Some applications of optimization in matrix theory. Linear Alg Appl 40:101–118

    Article  MATH  MathSciNet  Google Scholar 

  13. Zhao Q, Karisch SE, Rendl F, Wolkowicz H (1998) Semidefinite programming relaxations for the quadratic assignment problem. J Combin Optim 2:71–109

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department Combinatorics and Optimization, University Waterloo, Waterloo, Canada

    Henry Wolkowicz

Authors
  1. Henry Wolkowicz
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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

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© 2008 Springer-Verlag

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Wolkowicz, H. (2008). Duality for Semidefinite Programming . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_139

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