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Semi-infinite Programming, Semidefinite Programming and Perfect Duality

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Book cover Encyclopedia of Optimization

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Keywords

Duality of the Linear SIP Problem

Dual Semidefinite Programs

Perfect Duality from the View of Linear Semi-Infinite Programming

The SDP as a Conic Convex Program

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References

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References

  1. 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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. Charnes A, Cooper WW, Kortanek KO (1962) Duality, Haar programs and finite sequence spaces. Proc Nat Acad Sci USA 48:782–786

    Article  MathSciNet  Google Scholar 

  4. Charnes A, Cooper WW, Kortanek KO (1962) A duality theory for convex programs with convex constraints. Bull Amer Math Soc 68:605–608

    Article  MathSciNet  MATH  Google Scholar 

  5. Charnes A, Cooper WW, Kortanek KO (1963) Duality in semi-infinite programs and some works of Haar and Caratheodory. Managem Sci 9:208–228

    MathSciNet  Google Scholar 

  6. Charnes A, Cooper WW, Kortanek KO (1965) On representation of semi-infinite programs which have no duality gaps. Managem Sci 12:113–121

    MathSciNet  Google Scholar 

  7. Fiacco AV, Kortanek KO (eds) (1983) Semi-infinite programming and applications. Lecture Notes Economics and Math Systems. Springer, Berlin

    MATH  Google Scholar 

  8. Gustafson SÅ, Kortanek KO (1983) Semi-infinite programming and applications. In: Bachem A, Grötschel M, Korte B (eds) Mathematical Programming the State of the Art Bonn 1982. Springer, Berlin, pp 132–157

    Google Scholar 

  9. Gustafson S-å, Kortanek KO, Rom WO (1970) Non-Chebysevian moment problems. SIAM J Numer Anal 7:335–342

    Article  MathSciNet  MATH  Google Scholar 

  10. Hettich R (ed) (1979) Semi-infinite programming. Lecture Notes Control Inform Systems. Springer, Berlin

    MATH  Google Scholar 

  11. Hettich R, Kortanek KO (1993) Semi-infinite programming: theory, methods, and applications. SIAM Rev 35:380–429

    Article  MathSciNet  MATH  Google Scholar 

  12. Kortanek KO (1976) Perfect duality in generalized linear programming. In: Prékopa A (ed) Proc. IX Internat. Symp. on Math. Program., North Holland and Publ. House Hungarian Acad. Sci., 43–58

    Google Scholar 

  13. Kortanek KO (1977) Constructing a perfect duality in infinite programming. Appl Math Optim 3:357–372

    Article  MathSciNet  MATH  Google Scholar 

  14. Kortanek KO, Zhang Qinghong (2001) Perfect duality in semi-infinite and semidefinite programming. Math Program 91 1(127–144

    MathSciNet  MATH  Google Scholar 

  15. Luo Zhi-Quan, Sturm JF, Zhang Shuzhong (Apr. 1997) Duality results for conic convex programming. Techn. Report Econometric Inst. Erasmus Univ. 9719/A

    Google Scholar 

  16. Ramana MV (1997) An exact duality theory for semidefinite programming and its complexity implications. Math Program B 77:129–162, Semidefinite Programming, Edited by Michael Overton and Henry Wolkowitz.

    MathSciNet  Google Scholar 

  17. Ramana MV, Tunçel L, Wolkowicz H (1997) Strong duality for semidefinite programming. SIAM J Optim 7:641–662

    Article  MathSciNet  MATH  Google Scholar 

  18. Sturm JF (Sept. 1997) Primal-dual interior point approach to semidefinite programming. PhD Thesis Erasmus Univ. Rotterdam, The Netherlands,), Tinbergen Inst. Res. Ser. vol 156, Thesis Publ., Amsterdam, The Netherlands, 1997.

    Google Scholar 

  19. Vandenberghe L, Boyd S (1996) Semidefinite programming. SIAM Rev 38:49–95

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. University Iowa, Iowa City, USA

    K. O. Kortanek & Qinghong Zhang

Authors
  1. K. O. Kortanek
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  2. Qinghong Zhang
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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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Kortanek, K.O., Zhang, Q. (2008). Semi-infinite Programming, Semidefinite Programming and Perfect Duality . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_590

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