Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 61, 2012 - Issue 5
384
Views
14
CrossRef citations to date
0
Altmetric
Original Articles

Feasible direction method for bilevel programming problem

&
Pages 597-616 | Received 20 Feb 2009, Accepted 08 Nov 2011, Published online: 13 Dec 2011

References

  • Bard , JF . 1988 . Convex two-level optimization . Math. Prog. , 40 : 15 – 27 .
  • Bard , JF . 1991 . Some properties of the bilevel programming problem . J. Optim. Theory Appl. , 68 : 371 – 378 .
  • Bard , JF . 1998 . Practical Bilevel Optimization: Algorithms and Applications , Dordrecht : Kluwer Academic Publishers .
  • Dempe , S . 2002 . Foundations of Bilevel Programming , Dordrecht : Kluwer Academie Publishers .
  • Dempe , S and Dutta , J . Is bilevel programming a special case of a mathematical program with complementarity constraints? . Math. Prog. , (to appear)
  • Dempe , S and Schmidt , H . 1996 . On an algorithm solving two-level programming problems with nonunique lower level solutions . Comput. Optim. Appl. , 6 : 227 – 249 .
  • Dutta , J and Dempe , S . 2006 . “ Bilevel programming with convex lower level problems ” . In Optimization with Multivalued Mappings: Theory, Applications and Algorithms , Edited by: Dempe , S and Kalashnikov , V . 51 – 71 . New York : Springer Science+Business Media, LLC .
  • Fletcher , R and Leyffer , S . 2002 . Numerical experience with solving MPECs as NLPs , Tech. Rep. NA/210, Department of Mathematics, University of Dundee .
  • Floudas , CA , Pardalos , PM , Adjiman , CS , Esposito , WR , Gümüş , ZH , Harding , ST , Klepeis , JL , Meyer , CA and Schweiger , CA . 1999 . “ Handbook of Test Problems in Local and Global Optimization ” . In Nonconvex Optimization and its Applications , Vol. 33 , Dordrecht : Kluwer Academic Publishers .
  • Floudas , CA and Zlobec , S . 1998 . “ Optimality and duality in parametric convex lexicographic programming ” . In Multilevel Optimization: Algorithms and Applications , Edited by: Migdalas , A , Pardalos , PM and Värbrand , P . 359 – 379 . Dordrecht : Kluwer Academic Publishers .
  • Gauvin , J . 1977 . A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programming . Math. Prog. , 12 : 136 – 139 .
  • Hager , WW . 1979 . Lipschitz continuity for constrained processes . SIAM J. Control Optim. , 17 : 321 – 328 .
  • Kojima , M . 1980 . “ Strongly stable stationary solutions in non-linear programs ” . In Analysis and Computation of Fixed Points , Edited by: Robinson , SM . 93 – 138 . New York : Academic Press .
  • Leyffer , S . 2000 . MacMPEC AMPL collection of mathematical programs with equilibrium constraints , Argonne National Laboratory . Available at http://www-unix.mcs.anl.gov/~leyffer/MacMPEC
  • Luo , Z-Q , Pang , J-S and Ralph , D . 1996 . Mathematical Programs with Equilibrium Constraints , Cambridge : Cambridge University Press .
  • Mersha , AG and Dempe , S . 2006 . Linear bilevel programming with upper level constraints depending on the lower level solution . Appl. Math. Comput. , 180 : 247 – 254 .
  • Mifflin , R . 1977 . Semismooth and semiconvex functions in constrained optimization . SIAM J. Control Optim. , 15 : 959 – 972 .
  • Outrata , J , Kočvara , M and Zowe , J . 1998 . Nonsmooth Approach to Optimization Problems with Equilibrium Constraints , Dordrecht : Kluwer Academic Publishers .
  • Ralph , D and Dempe , S . 1995 . Directional derivatives of the solution of a parametric non-linear program . Math. Prog. , 70 : 159 – 172 .
  • Scheel , H and Scholtes , S . 2000 . Mathematical programs with equilibrium constraints: stationarity, optimality, and sensitivity . Math. Oper. Res. , 25 : 1 – 22 .
  • Scholtes , S . 1994 . Introduction to piecewise differentiable equations , Tech. Rep. No. 53/1994, Universität Karlsruhe, Institut für Statistik und Mathematische Wirtschaftstheorie . Available at http://www.eng.cam.ac.uk/~ss248/publications/index.html
  • Scholtes , S . 2001 . Convergence properties of a regularization scheme for mathematical programs with complementarity constraints . SIAM J. Optim. , 11 : 918 – 936 .
  • Topkis , DM and Veinott , AFjun . 1967 . On the convergence of some feasible direction algorithms for non-linear programming . SIAM J. Control Optim. , 5 : 268 – 279 .
  • Tuy , H , Migdalas , A and Hoai-Phuong , NT . 2007 . A novel approach to bilevel non-linear programming . J. Glob. Optim. , 38 : 527 – 554 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.