Merit functions and descent algorithms for a class of variational inequality problems

Optimization

Volumn 41, Issue 1, 1997, Pages 37-55

  Patriksson, M ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

Author keywords

Cost approximation; Descent algorithms; Fenchel's inequality; Merit functions; Variational inequality problems

Indexed keywords

EID: 0040747874     PISSN: 02331934     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331939708844324     Document Type: Article

References (24)

1. Auchmuty, G. (1989). Variational principles for variational inequalities, Numerical Functional Analysis and Optimization, 10, 863-874.
2. Céa, J. (1978). Optimization: Theory and Algorithms, Springer-Verlag, Berlin.
3. Clarke, F. H. (1983). Optimization and Nonsmooth Analysis, John Wiley & Sons, New York, NY.
4. Ekeland, I. and Temam, R. (1976). Convex Analysis and Variational Problems, North-Holland, Amsterdam.
5. Fang, S.-C. and Peterson, E. L. (1982). Generalized variational inequalites, Journal of Optimization Theory and Applications, 38, 363-383.
6. Fenchel, W. (1949). On conjugate convex functions, Canadian Journal of Mathematics, 1, 73-77.
7. Fukushima, M. (1992). Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems, Mathematical Programming, 53, 99-110.
8. 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.
9. Hogan, W. W. (1973). Point-to-set maps in mathematical programming, SIAM Review, 15, 591-603.
10. Karamardian, S. (1971). Generalized complementarity problem, Journal of Optimization Theory and Applications, 8, 161-168.
11. Kinderlehrer, D. and Stampacchia, G. (1980). An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, NY.
12. Larsson, T. and Patriksson, M. (1994). A class of gap functions for variational inequalities, Mathematical Programming, 64, 53-79.
13. Minty, G. J. (1962). Monotone (nonlinear) operators in Hilbert space, Duke Mathematical Journal, 29, 341-346.
14. Murchland, J. D. (1970). Road network traffic distribution in equilibrium, In: Mathematical Models in the Social Sciences, II Oberwolfach-Tagung über Operations Research, Mathematisches Forschungsinstitut, Oberwolfach, 20-25 October 1969, Henn, R., Künzi, H. P. and Schubert, H. (eds.), Anton Hain Verlag, Meisenheim am Glan, West Germany, pp. 145-183, In German, translation by Paul, H. A.
15. Noor, M. A. (1991). Some classes of variational inequalities, In: Constantin Carathéodory: An international tribute, Th. M. Rassias (ed.), World Scientific Publ. Co., Singapore, pp. 996-1019.
16. Patriksson, M. (1993). Partial linearization methods in nonlinear programming, Journal of Optimization Theory and Applications, 78, 227-246.
17. Patriksson, M. (1993). A unified description of iterative algorithms for traffic equilibria, European Journal of Operational Research, 71, 154-176.
18. Patriksson, M. (1993). A unified framework of descent algorithms for nonlinear programs and variational inequalities, Ph.D. dissertation, Department of Mathematics, Linköping Institute of Technology, Linköping, Sweden.
19. Patriksson, M. (1994). On the convergence of descent methods for monotone variational inequalities, Operations Research Letters, 16, 265-269.
20. Robinson, S. M. (1979). Generalized equations and their solutions, part I: basic theory, Mathematical Programming Study, 10, 128-141.
21. Rockafellar, R. T. (1970). Convex Analysis, Princeton University Press, Princeton, NJ.
22. Rockafellar, R. T. (1981). The Theory of Subgradients and Its Applications to Problems of Optimization: Convex and Nonconvex Functions, Heldermann Verlag, Berlin.
23. Zangwill, W. I. (1969). Nonlinear Programming: A Unified Approach, Prentice-Hall, Englewood Cliffs, NJ.
24. Zhu, D. L. and Marcotte, P. (1993). Modified descent methods for solving the monotone variational inequality problem, Operations Research Letters, 14, 111-120.