Optimality Conditions for a Class of Mathematical Programs with Equilibrium Constraints

Published Online:https://doi.org/10.1287/moor.24.3.627

References

  • Anandalingam G., Friesz T. Hierarchical optimization. Ann. Oper. Res. (1992) 34(Editors.)CrossrefGoogle Scholar
  • Aubin J.-P., Frankowska H.Set-Valued Analysis (1990) (Birkhäuser, Boston) Google Scholar
  • Clarke F. H.Optimization and Nonsmooth Analysis (1983) (Wiley, New York) Google Scholar
  • Kočvara M., Outrata J. V., Du D., Qu L., Womersley R. On the solution of optimum design problems with variational inequalities. Recent Advances in Nonsmooth Optimization (1995) (World Scientific, Singapore) 172–192CrossrefGoogle Scholar
  • Kočvara M., Outrata J. V., Ferris M., Pang J.-S. A nonsmooth approach to optimization problems with equilibrium constraints. Complementarity and Variational Problems (1997) (SIAM, Philadelphia, PA) 148–164Google Scholar
  • Kuntz L., Scholtes S. A nonsmooth variant of the Mangasarian-Fromovitz constraint qualification. J. Optim. Theory Appl. (1994) 82:59–75CrossrefGoogle Scholar
  • Luo Z.-Q., Pang J.-S., Ralph D.Mathematical Programs with Equilibrium Constraints (1996) (Cambridge University Press, Cambridge, UK) CrossrefGoogle Scholar
  • Luo Z.-Q., Pang J.-S., Ralph D., Wu S.-Q. Exact penalization and stationary conditions of mathematical programs with equilibrium constraints. Math. Programming (1996) 75:19–76CrossrefGoogle Scholar
  • Mordukhovich B. S.Approximation Methods in Problems of Optimization and Control (1988) (Nauka, Moscow, Russia. (in Russian; 2nd English edition to appear in Wiley-Interscience)) Google Scholar
  • Mordukhovich B. S. Generalized differential calculus for nonsmooth and set-valued mappings. J. Math. Anal. Appl. (1994) 183:250–288CrossrefGoogle Scholar
  • Murty K. G.Linear Complementarity, Linear and Nonlinear Programming (1988) (Heldermann, Berlin) Google Scholar
  • Outrata J. V. On optimization problems with variational inequality constraints. SIAM J. Optim. (1994) 4:340–357CrossrefGoogle Scholar
  • Robinson S. M. Strongly regular generalized equations. Math. Oper. Res. (1980) 5:43–62LinkGoogle Scholar
  • Treiman J. S. General optimality conditions for bi-level optimization problems. (1997) . PreprintGoogle Scholar
  • Ye J. J. Optimality conditions for optimization problems with complementarity constraints. SIAM J. Optim. (1999) 9:374–387CrossrefGoogle Scholar
  • Ye J. J., Ye X. Y. Necessary optimality conditions for optimization problems with variational inequality constraints. Math. Oper. Res. (1997) 22:977–997LinkGoogle Scholar
  • Ye J. J., Zhu D. L. Optimality conditions for bilevel programming problems. Optimization (1995) 33:9–27CrossrefGoogle Scholar
  • Ye J. J., Zhu D. L., Zhu Q. J. Exact penalization and necessary optimality conditions for generalized bilevel programming problems. SIAM J. Optim. (1997) 7:481–507CrossrefGoogle Scholar
  • Zhang R. Problems of hierarchical optimization in finite dimensions. SIAM J. Optim. (1995) 4:521–536CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.