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Original Articles

A successive linear programming algorithm for nonsmooth monotone variational inequalities

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Pages 29-35 | Received 01 Dec 2008, Published online: 16 Oct 2009

References

  • Auslender , A. 1976 . Optimization: méthodes numériques , Paris : Masson .
  • Browder , F. E. 1966 . Existence and approximation of solutions of nonlinear variational inequalities . Proc. Natl Acad. Sci. USA , 56 : 1080 – 1086 .
  • Cohen , G. 1988 . Auxiliary problem principle extended to variational inequalities . J. Optim. Theory Appl. , 59 : 325 – 333 .
  • Facchinei , F. and Pang , J. S. 2003 . Finite–dimensional Variational Inequalities and Complementarity Problems , New York : Springer–Verlag .
  • Fukushima , M. 1992 . Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems . Math. Program. , 53 : 99 – 110 .
  • Gaudioso , M. , Giallombardo , G. and Miglionico , G. 2006 . An incremental method for solving convex finite min-max problems . Math. Oper. Res. , 31 : 173 – 187 .
  • Harker , P. T. and Pang , J. S. 1990 . Finite–dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications . Math. Program. , 48 : 161 – 220 .
  • Kiwiel , K. C. 2006 . A proximal bundle method with approximate subgradient linearizations . SIAM J. Optim. , 16 : 1007 – 1023 .
  • Hiriart-Urruty , J. B. and Lemarechal , C. 1993 . Convex Analysis and Minimization Algorithms , Berlin : Springer .
  • Marcotte , P. 1985 . A new algorithm for solving variational inequalities with application to the traffic assignment problem . Math. Program. , 33 : 339 – 351 .
  • Marcotte , P. and Dussault , J. P. 1989 . A sequential linear programming algorithm for solving monotone variational inequalities . SIAM J. Control Optim. , 27 : 1260 – 1278 .
  • Nguyen , S. and Dupuis , C. 1984 . An efficient method for computing traffic equilibria in networks with asymmetric transportation costs . Transport. Sci. , 18 : 185 – 202 .
  • Taji , K. and Fukushima , M. 1996 . A new merit function and successive quadratic programming algorithm for variational inequality problems . SIAM J. Optim. , 6 : 704 – 713 .
  • Taji , K. , Fukushima , M. and Ibaraki , T. 1993 . A globally convergent Newton method for solving strongly monotone variational inequalities . Math. Program. , 58 : 369 – 383 .
  • Zhu , D. L. and Marcotte , P. 1994 . An extended descent framework for variational inequalities . J. Optim. Theory Appl. , 80 : 349 – 366 .
  • Zhu , D. L. and Marcotte , P. 1993 . Modified descent methods for solving the monotone variational inequality problem . Oper. Res. Lett. , 14 : 111 – 120 .

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