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Original Articles

An interior-point smoothing technique for Lagrangian relaxation in large-scale convex programmingFootnote

Pages 183-200 | Received 31 Aug 2006, Accepted 04 May 2007, Published online: 27 Oct 2009

References

  • Fukuda , M , Kojima , M and Shida , M . 2002 . Lagrangian dual interior-point methods for semidefinite programs . SIAM J. Optim. , 12 : 1007 – 1031 .
  • Goffin , JL . 1997 . Solving non-linear multicommodity flow problems by the analytic center cutting plane method . Math. Prog. , 76 : 131 – 154 .
  • Goffin , JL , Haurie , A and Vial , JP . 1992 . Decomposition and non-differentiable optimization with the projective algorithm . Manage. Sci. , 38 : 284 – 302 .
  • Goffin , JL and Vial , JP . 2002 . Convex non-differentiable optimization: A survey focussed on the analytic center cutting plane method . Optim. Methods Software , 17 : 805 – 867 .
  • Gondzio , J , Du Merle , O Sarkissian , R . 1996 . ACCPM–a library for convex optimization based on an analytic center cutting plane method . Euro. J. Oper. Res. , 94 : 206 – 211 .
  • Huard , P . 1967 . “ Resolution of mathematical programming with non-linear constraints by the methods of centers ” . In Nonlinear Programming , Edited by: Abadie , J . 209 – 222 . Amsterdam : North-Holland .
  • Kachiyan , LG and Todd , MJ . 1993 . On the complexity of approximating the maximal inscribed ellipsoid for a polytope . Math. Prog. , 61 : 137 – 160 .
  • Kojima , M , Megiddo , N Mizuno , S . 1993 . Horizontal and vertical decomposition in interior point methods for linear programs , Technical report, Information Sciences, Tokyo Institute of Technology .
  • Lasdon , LS . 1970 . Optimization Theory for Large Systems , New York : The Macmillan Company .
  • Nesterov , Y and Nemirovskii , A . 1994 . Interior-Point Polynomial Algorithms in Convex Programming , Philadelphia : SIAM .
  • Shida , M , Shindoh , S and Kojima , M . 1997 . Centers of monotone generalized complementarity problems . Math. Oper. Res. , 22 : 969 – 976 .
  • Sonnevend , G . 1986 . New algorithms in convex programming beased on a notion of ‘centre’ (for systems of analytic inequalities) and on rational extrapolation , K.H. Hoffmann, J.B. Hiriat-Urruty, C. Lemarechal and J. Zowe, eds., Germany, April : in Trends in Mathematical Optimization, Proceeding of the 4-th French-German Conference on Optimization in Irsee . International Series of Numerical Mathematics 84, Birkhäuser Verlag, Basel, Switzerland, 1998, pp. 311–327
  • Vaidya , PM . 1996 . A new algorithm for minimizing convex functions over convex sets . Math. Prog. , 73 : 291 – 341 .
  • Zhao , G . 1999 . Interior-point methods with decomposition for solving large-scale linear programs . J. Optim. Theory Appl. , 102 : 169 – 192 .
  • Zhao , G . 2001 . A log-barrier method with Benders decomposition for solving two-stage stochastic programs . Math. Prog. , 90 : 507 – 536 .
  • Zhao , G . 2005 . A Lagrangian dual method with self-concordant barriers for multi-stage stochastic convex programming . Math. Prog. , 102 : 1 – 24 .

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