On Zero Duality Gap and the Farkas Lemma for Conic Programming

Published Online:https://doi.org/10.1287/moor.1080.0339

References

  • Anger B., Lembcke J. Hahn-Banach type theorems for hypolinear functionals. Math. Ann. (1974) 209:127–151CrossrefGoogle Scholar
  • Arrow K. J., Hurwicz L., Uzawa H. Studies in linear and nonlinear programming. Stanford Mathematical Studies in the Social Sciences (1958) II(Stanford University Press, Stanford, CA) Google Scholar
  • Borwein J. M., Lewis A. S. Partially finite convex programming. I. Quasi relative interiors and duality theory. Math. Programming (1992) 57(1, Ser. B):15–48CrossrefGoogle Scholar
  • Cheney W. Analysis for applied mathematics. Graduate Texts in Mathematics (2001) 208(Springer-Verlag, New York) Google Scholar
  • Clark S. A. Arbitrage approximation theory. J. Math. Econom. (2000) 33(2):167–181CrossrefGoogle Scholar
  • Clark S. A. An infinite-dimensional LP duality theorem. Math. Oper. Res. (2003) 28(2):233–245LinkGoogle Scholar
  • Clark S. A. Necessary and sufficient conditions for solving infinite-dimensional linear inequalities. Positivity (2006) 10(3):475–489CrossrefGoogle Scholar
  • de Klerk E., Roos C., Terlaky T.Nonlinear Optimization. Lecture Notes (2003) (University of Technology, Delft, The Netherlands) Google Scholar
  • Holmes R. B. Geometric functional analysis and its applications. Graduate Texts in Mathematics (1975) 24(Springer-Verlag, New York) Google Scholar
  • Jeyakumar V., Floudas C. A., Pardalos P. M. Farkas lemma: Generalizations. Encyclopedia of Optimization (2001) II(Kluwer Academic Publishers, Dordrecht, The Netherlands) 87–91CrossrefGoogle Scholar
  • Lasserre J. B. A Farkas lemma without a standard closure condition. SIAM J. Control Optim. (1997) 35(1):265–272CrossrefGoogle Scholar
  • Luo Z.-Q., Sturm J. F., Zhang S. Duality and self-duality for conic convex programming. (1996) . Technical Report 9620/A, Econometric Institute, Erasmus University, Rotterdam, The NetherlandsGoogle Scholar
  • Nemirovski A. Advances in convex optimization: Conic programming. International Congress of Mathematicians, Vol. I. Eur. Math. Soc. (2007) (Zürich, Switzerland)413–444CrossrefGoogle Scholar
  • Nesterov Y., Nemirovskii A. Interior-point polynomial algorithms in convex programming. SIAM Studies in Applied Mathematics (1994) 13(Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA) CrossrefGoogle Scholar
  • Pólik I., Terlaky T. Exact duality for optimization over symmetric cones. (2007) . Technical Report AdvOL 10, Advanced Optimization Laboratory, McMaster University, Hamilton, Ontario, CanadaGoogle Scholar
  • Ramana M. V. An exact duality theory for semidefinite programming and its complexity implications. Math. Programming (1997) 77(2, Ser. B):129–162CrossrefGoogle Scholar
  • Rockafellar R. T.Convex Analysis (1970) 28(Princeton University Press, Princeton, NJ) Princeton Mathematical SeriesCrossrefGoogle Scholar
  • Shapiro A. On duality theory of conic linear problems. Semi-Infinite Programming (Alicante 1999). Nonconvex Optim. Appl. (2001) 57(Kluwer Acad. Publ., Dordrecht, The Netherlands) 135–165CrossrefGoogle Scholar
  • Simons S. Extended and sandwich versions of the Hahn-Banach theorem. J. Math. Anal. Appl. (1968) 21:112–122CrossrefGoogle Scholar
  • Zălinescu C. A generalization of the Farkas lemma and applications to convex programming. J. Math. Anal. Appl. (1978) 66(3):651–678CrossrefGoogle Scholar
  • Zălinescu C. Solvability results for sublinear functions and operators. Z. Oper. Res. Ser. A–B (1987) 31(3):A79–A101CrossrefGoogle Scholar
  • Zălinescu C.Convex Analysis in General Vector Spaces (2002) (World Scientific Publishing Co., Inc., River Edge, NJ) CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.