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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 58, 2009 - Issue 8
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Original Articles

Bilevel convex programming models

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Pages 1009-1028 | Received 23 Jun 2006, Accepted 23 Jul 2007, Published online: 02 Nov 2009

References

  • Bank , B . 1982 . Non-Linear Parametric Optimization , Berlin : Akademie-Verlag .
  • Bard , JF . 1983 . An efficient point algorithm for a linear two-stage optimization problem . Oper. Res. , 31 : 670 – 684 .
  • Bard , JF . 1984 . Optimality conditions for the bilevel programming problem . Naval Res. Logist. Q. , 31 : 13 – 26 .
  • Bard , JF . 1988 . Convex two-level optimization . Math. Program. , 40 : 15 – 27 .
  • Bard , JF and Falk , JE . 1982 . An explicit solution to the multilevel programming problem . Comput. Oper. Res. , 9 : 77 – 100 .
  • Baumgart , R and Beer , K . 1992 . A practicable way for computing the directional derivative of the optimal value function in convex programming . Optimization , 25 : 379 – 389 .
  • Dempe , S . 1992 . A necessary and sufficient optimality condition for bilevel programming problems . Optimization , 25 : 341 – 354 .
  • Dempe , S . 1993 . “ On the leader's dilemma and a new idea for attacking bilevel programming problems ” . In Tech. rep., Fachbereich Mathematik , Chemnitz, , Germany : Technische Universitat Chemnitz .
  • Dempe , S . 1995 . Computing optimal incentives via bilevel programming . Optimization , 33 : 29 – 42 .
  • Dempe , S . 2003 . Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints . Optimization , 52 : 333 – 359 .
  • Floudas , CA and Zlobec , S . 1998 . “ Optimality and duality in parametric lexicographic convex programming ” . In Multilevel Optimization: Algorithms and Applications , Edited by: Migdalas , A , Pardalos , PM and Varbrand , P . Dordrecht, , The Netherlands : Kluwer Academic .
  • Haurie , A , Savard , G and White , DJ . 1990 . A note on: An efficient point algorithm for a linear two-stage optimization problem . Oper. Res. , 38 : 553 – 555 .
  • Hogan , WW . 1973 . Directional derivatives for the extremal-value functions with applications to the completely convex case . Oper. Res. , 21 ( 1 ) : 188 – 209 .
  • Loridan , P and Morgan , J . 1989 . A theoretical approximation scheme for stackelberg problems . J. Optim. Theory Appl. , 61 ( 1 ) : 95 – 110 .
  • Trujillo-Cortez , R . 1997 . “ LFS functions in stable bilevel programming ” . In Master's thesis, Department of Mathematics and Statistics , Montreal, , Canada : McGill University .
  • Trujillo-Cortez , R . 2000 . “ Stable convex parametric programming and applications ” . In Ph.D. thesis, Department of Mathematics and Statistics , Montreal : McGill University .
  • Trujillo-Cortez , R and Zlobec , S . 2001 . Stability and optimality in parametric convex programming models . Math. Commun. , 6 ( 2 ) : 107 – 121 .
  • Ye , JJ and Zhu , DL . 1995 . Optimality conditions for bilevel programming problems . Optimization , 33 : 9 – 27 .
  • Zlobec , S . 1988 . Characterizing optimality in mathematical programming models . Acta Appl. Math. , 12 : 113 – 180 .
  • Zlobec , S . 1991 . The marginal value formula in input optimization . Optimization , 22 : 341 – 386 .
  • Zlobec , S . 2001 . Stability in linear programming models: An index set approach . Ann. Oper. Res.: Optimization with Data Perturbations , II : 363 – 382 .
  • Zlobec , S . 2001 . “ Stable Parametric Programming ” . In Series: Applied Optimization , Vol. 57 , Dordrecht, , The Netherlands : Kluwer Academic Series .

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