A Merit Function for Variational Inequalities Applied to Equilibrium Problems

• Auchmuty, G. (1989). Variational principles for variational inequalities. Numer. Funct. Anal. Optim., 10, 863–874.

  Google Scholar 

• Auslender, M. (1976). Optimisation: Méthodes Numériques. Masson, Paris.

  Google Scholar 

• Bertsekas, D.P. (1982). Constrained Optimization and Lagrange Multiplier Methods. Academic Press, New York.

  Google Scholar 

• Bertsekas, D.P. and Tsitsiklis, J.N. (1989). Parallel and Distributed Computation. Prentice-Hall, Englewood Cliffs.

  Google Scholar 

• Bertsekas, D.P. (1995). Nonlinear Programming. Athena Scientific, Belmont.

  Google Scholar 

• Dennis, J.E. and Schnabel, R.B. (1983) Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs.

  Google Scholar 

• Eaves, B.C. (1985). Finite solution of pure trade markets with Cobb–Douglas utilities. Mathematical Programming Study, 23, 226–239.

  Google Scholar 

• Fukushima, M. (1992). Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems. Mathematical Programming, 53, 99–110.

  Google Scholar 

• Gabay, D. (1983). Applications of the method of multipliers to variational inequalities. In M. Fortin and R. Glowinski (eds.), Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, 299–331. North-Holland, Amsterdam.

  Google Scholar 

• Harker, P.T. (1984). A variational inequality approach for the determination of oligopolistic market equilibrium. Mathematical Programming, 30, 105–111.

  Google Scholar 

• Harker, P.T. and Pang, J-S. (1990). Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming, 48, 161–220.

  Google Scholar 

• Kanzow, C. and Jiang, H. (1998). A continuation method for (strongly) monotone variational inequalities. Mathematical Programming, 81, 103–125.

  Google Scholar 

• Kanzow, C. and Kleinmichel, H. (1995). A class of Newton-type methods for equality and inequality constrained optimization. Optimization Methods and Software, 5, 173–198.

  Google Scholar 

• Larsson, L. and Patriksson, M. (1994). A class of gap functions for variational inequalities. Mathematical Programming, 64, 53–79.

  Google Scholar 

• Magnanti, T.L. and Perakis, G. (1997). The orthogonality theorem and the strong-F-monotonicity condition for variational inequality algorithms, Siam J. Optimization, 7, 248–273.

  Google Scholar 

• Nagurney, A. (1993). Network Economics. Kluwer Academic Publishers, London.

  Google Scholar 

• Pang, J-S. (1991). A B-differentiable equation-based, globally and locally quadratically convergent algorithm for nonlinear programs, complementarity and variational inequality problems, Mathematical Programming, 51, 101–131.

  Google Scholar 

• Polak, E. and Qi, L. (1998). Globally and superlinearly convergent algorithm for minimizing a normal merit function. Siam J. Control Optim., 36, 1005–1019.

  Google Scholar 

• Qi, L. and Jiang, H. (1997). Semismooth Karush–Khun–Tucker equations and convergence analysis of Newton and quasi-Newton methods for solving these equations, Math. Oper. Res., 22, 301–325.

  Google Scholar 

• Taji, K., Fukushima, M. and Ibaraki, T. (1993). A globally convergent Newton method for solving strongly monotone variational inequalities, Mathematical Programming, 58, 369–383.

  Google Scholar 

• Taji, K. and Fukushima, M. (1996). A new merit function and a successive quadratic programming algorithm for variational inequality problems. Siam J. Optimization, 6, 704–713.

  Google Scholar 

• Zhu, D.L. and Marcotte, P. (1996). Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities. Siam J. Optimization, 6, 714–726.

  Google Scholar 

Download references