Modified primal path-following scheme for the monotone variational inequality problem

Journal of Optimization Theory and Applications

Volumn 95, Issue 1, 1997, Pages 189-208

  Wu, J H ^a,b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b INRO Consultants   (Canada)

Author keywords

Barrier function method; Interior point method; Mathematical programming; Network equilibrium problem; Path following method; Variational inequalities

Indexed keywords

FUNCTIONS; LINEAR PROGRAMMING;

BARRIER FUNCTION METHOD; BARRIERS FUNCTIONS; EQUILIBRIUM PROBLEM; FUNCTION METHODS; INTERIOR-POINT METHOD; NETWORK EQUILIBRIUM; NETWORK EQUILIBRIUM PROBLEM; PATH FOLLOWING; PATH-FOLLOWING METHOD; VARIATIONAL INEQUALITIES;

VARIATIONAL TECHNIQUES;

EID: 0031487170     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022643630525     Document Type: Article

References (21)

1. PANG, J. S., Complementarity Problems, Handbook of Global Optimization, Edited by R. Horst and P. M. Pardalos, Kluwer Academic Publishers, Dordrecht, Netherlands, pp. 284-313, 1995.
2. TSENG, P., Global Linear Convergence of a Path-Following Algorithm for Some Monotone Variational Inequality Problems, Journal of Optimization Theory and Applications, Vol. 75, pp. 265-279, 1992.
3. WU, J. H., Interior-Point Algorithms for Some Monotone Variational Inequality Problems, Publication 879, Centre de Recherche sur les Transports, Université de Montréal, 1993.
4. WU, J. H., A Long-Step Primal Path-Following Algorithm for Some Monotone Variational Inequality Problems, Publication 959, Centre de Recherche sur les Transports, Université de Montréal, 1993.
5. TAJI, K., FUKUSHIMA, M., and IBARAKI, T., A Globally Convergent Newton Method for Solving Monotone Variational Inequalities, Mathematical Programming, Vol. 58, pp. 369-383, 1993.
6. KORTANEK, K. O., and ZHU, J., A Polynomial Barrier Algorithm for Linearly Constrained Convex Programming Problems, Mathematics of Operations Research, Vol. 1, pp. 116-127, 1993.
7. WU, J. H., RUBIO-ARDANAZ, J. M., and FLORIAN, M., A Primal Path-Following Algorithmic Scheme for the Monotone Variational Inequality Problem with One Simple Constraint and Nonnegative Variables: Implementation and Computational Experiences, Publication CRT-95-39, Centre de Recherche sur les Transports, Université de Montréal, 1995.
8. FIACCO, A. V., and MCCORMICK, G. P., Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley and Sons, New York, New York, 1968.
9. WRIGHT, M. H., Interior Methods for Constrained Optimization, Acta Numerica, pp. 341-407, 1992.
10. GÜLER, O., Existence of Interior Points and Interior Paths in Nonlinear Monotone Complementarity Problems, Mathematics of Operations Research, Vol. 1, pp. 128-147, 1993.
11. Wu, J. H., FLORIAN, M., and MARCOTTE, P., A General Descent Framework for Monotone Variational Inequality Problems, Mathematical Programming, Vol. 61, pp. 281-300, 1993.
12. NESTEROV, Y., and NEMIROVSKII, A., Interior-Point Polynomial Algorithms in Convex Programming, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, Pennsylvania, 1994.
13. BERTSEKAS, D. P., and GAFNI, E. M., Projection Methods for Variational Inequalities with Application to the Traffic Assignment Problem, Mathematical Programming Study, Vol. 17, pp. 139-159, 1982.
14. CHOI, I. C., and GOLDFARB, D., Exploiting Special Structure in a Primal-Dual Path-Following Algorithm, Mathematical Programming, Vol. 58, pp. 33-52, 1993.
15. LAWPHONGPANICH, S., and HEARN, D. W., Simplicial Decomposition of the Asymmetric Traffic Assignment Problem, Transportation Research, Vol. 18B, pp. 123-133, 1984.
16. WU, J. H., and FLORIAN, M., A Simplicial Decomposition Method for the Transit Equilibrium Assignment Problem, Annals of Operations Research, Vol. 44, pp. 245-260, 1993.
17. PINAR, M. C., and ZENOIS, S. A., Parallel Decomposition of Multicommodity Network Flows Using Linear-Quadratic Penalty Algorithms, ORSA Journal on Computing, Vol. 4, pp. 235-248, 1992.
18. FUKUSHIMA, M., Equivalent Differentiable Optimization Problems and Descent Methods for Asymmetric Variational Inequality Problems, Mathematical Programming, Vol. 53, pp. 99-110, 1992.
19. KARMARKAR, N., A New Polynomial-Time Algorithm for Linear Programming, Combinatorica, Vol. 4, pp. 373-395, 1984.
20. YE, Y., and POTRA, F., An Interior-Point Algorithm for Solving Entropy Optimization Problems with Globally Linear and Locally Quadratic Convergence Rate, SIAM Journal on Optimization, Vol. 3, pp. 843-860, 1993.
21. ZANGWILL, W. I., Nonlinear Programming, Prentice-Hall, Englewood Cliffs, New Jersey, 1969.