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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 61, 2012 - Issue 12
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Original Articles

Stability of the primal-dual partition in linear semi-infinite programming

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Pages 1449-1465 | Received 15 Jul 2010, Accepted 23 Feb 2011, Published online: 03 May 2011

References

  • Ben-Israel , A , Charnes , A and Kortanek , KO . 1969 . Duality and asymptotic solvability over cones . Bull. Am. Math. Soc. , 75 : 318 – 324 .
  • Brosowski , B . 1982 . Parametric Semi-Infinite Optimization , Verlag Peter Lang, Frankfurt am Main – Bern .
  • Brosowski , B . 1984 . Parametric semi-infinite linear programming I. Continuity of the feasible set and the optimal value . Math. Program. , 21 : 18 – 42 .
  • Cánovas , MJ , Dontchev , AL , López , MA and Parra , J . 2005 . Metric regularity of semi-infinite constraint systems . Math. Program. , 104B : 329 – 346 .
  • Cánovas , MJ , Klatte , D , López , MA and Parra , J . 2007 . Metric regularity in convex semi-infinite optimization under canonical perturbations . SIAM J. Optim. , 18 : 717 – 732 .
  • Cánovas , MJ , López , MA and Parra , J . 2002 . Upper semicontinuity of the feasible set mapping for linear inequality systems . Set-Valued Anal. , 10 : 361 – 378 .
  • Cánovas , MJ , López , MA , Parra , J and Toledo , FJ . 2005 . Distance to ill-posedness and consistency value of linear semi-infinite inequality systems . Math. Program. , 103A : 95 – 126 .
  • Cánovas , MJ , López , MA , Parra , J and Toledo , FJ . 2006 . Distance to ill-posedness in linear optimization via the Fenchel-Legendre conjugate . J. Optim. Theory Appl. , 130 : 173 – 183 .
  • Cánovas , MJ , López , MA , Parra , J and Toledo , FJ . 2006 . Ill-posedness with respect to the solvability in linear optimization . Linear Algebra Appl. , 416 : 520 – 540 .
  • Charnes , A , Cooper , WW and Kortanek , KO . 1962 . Duality, Haar programs, and finite sequence spaces . Proc. Natl. Acad. Sci. USA , 48 : 783 – 786 .
  • Charnes , A , Cooper , WW and Kortanek , KO . 1963 . Duality in semi-infinite programs and some works of Haar and Carathéodory . Management Sci. , 9 : 209 – 228 .
  • Charnes , A , Cooper , WW and Kortanek , KO . 1965 . On representations of semi-infinite programs which have no duality gaps . Management Sci. , 12 : 113 – 121 .
  • Daniel , JW . 1975 . Remarks on perturbations in linear inequalities . SIAM J. Numer. Anal. , 12 : 770 – 772 .
  • Fischer , T . 1983 . Contributions to semi-infinite linear optimization . Meth. Verf. Math. Phys. , 27 : 175 – 199 .
  • Goberna , MA , Larriqueta , M and Vera , VN . 2003 . On the stability of the boundary of the feasible set in linear optimization . Set-Valued Anal. , 11 : 203 – 223 .
  • Goberna , MA and López , MA . 1998 . Linear Semi-Infinite Optimization , Wiley, Chichester .
  • Goberna , MA , López , MA and Todorov , MI . 1996 . Stability theory for linear inequality systems . SIAM J. Matrix Anal. , 17 : 730 – 743 .
  • Goberna , MA , López , MA and Todorov , MI . 1997 . Stability theory for linear inequality systems II: upper semicontinuity of the solution set mapping . SIAM J. Optim. , 7 : 1138 – 1151 .
  • Goberna , MA , López , MA and Todorov , MI . 2001 . On the stability of the feasible set in linear optimization . Set-Valued Anal. , 9 : 75 – 99 .
  • Goberna , MA and Todorov , MI . 2007 . Primal, dual and primal-dual partitions in continuous linear semi-infinite programming . Optimization , 56 : 617 – 628 .
  • Goberna , MA and Todorov , MI . 2008 . Generic primal-dual solvability in continuous linear semi-infinite programming . Optimization , 57 : 239 – 248 .
  • Goberna , MA and Todorov , MI . 2009 . Primal-dual stability in continuous linear optimization . Math. Program. , 116B : 129 – 146 .
  • Hiriart , U and Lemaréchal , C . 2000 . Fundamentals of Convex Analysis , New York : Springer-Verlag .
  • Jongen , HTh and Rückmann , JJ . 1998 . “ On stability and deformation in semi-infinite optimization ” . In Semi-Infinite Programming , Edited by: Reemtsen , R and Rückmann , JJ . 29 – 67 . Dordrecht : Kluwer Academic Publishers .
  • K.O. Kortanek, On the 1962–1972 decade of semi-infinite programming: a subjective view, in Semi-Infinite Programming: Recent Advances, M.A. Goberna, and M.A. López eds., Kluwer, Dordrecht, 2001, pp. 3–34.
  • Kortanek , KO and Zhang , Q . 2001 . Perfect duality in semi-infinite and semi-definite programming . Math. Program. , 91A : 127 – 144 .
  • León , T and Vercher , E . “ Optimization under uncertainty and linear semi-infinite programming: A survey ” . In Semi-Infinite Programming: Recent Advances Edited by: Goberna , MA and López , MA . 327 – 348 . Kluwer, Dordrecht
  • Robinson , SM . 1975 . Stability theory for systems of inequalities. Part I: Linear systems . SIAM J. Numer. Anal. , 12 : 754 – 769 .
  • Robinson , SM . 1976 . Stability theory for systems of inequalities. Part II: Differentiable non-linear systems . SIAM J. Numer. Anal. , 13 : 497 – 513 .
  • Rockafellar , RT . 1970 . Convex Analysis , Princeton, University Press .
  • Shapiro , A . 2001 . “ On duality theory of conic linear problems ” . In Semi-Infinite Programming: Recent Advances Edited by: Goberna , MA and López , MA . 135 – 165 . Kluwer, Dordrecht
  • Shapiro , A . 2005 . On duality theory of convex semi-infinite programming . Optimization , 54 : 535 – 543 .
  • Sturm , JF . 2000 . Theory and algorithms of semidefinite programming. High performance optimization . Appl. Optim. , 33 : 1 – 194 .
  • Todorov , MI . 1985–86 . Generic existence and uniqueness of the solution set to linear semi-infinite optimization problems . Numer. Funct. Anal. Optim. , 8 : 541 – 556 .
  • Tuy , H . 1977 . Stability property of a system of inequalities . Math. Oper. Statist. Series Opt. , 8 : 27 – 39 .

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