Gap functions for equilibrium problems

Journal of Global Optimization

Volumn 27, Issue 4, 2003, Pages 411-426

  Mastroeni, G ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

Descent methods; Equilibrium problems; Gap functions; Variational inequalities

Indexed keywords

ALGORITHMS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; OPTIMIZATION; THEOREM PROVING;

DESCENT METHOD; EQUILIBRIUM PROBLEM; GAP FUNCTION; VARIATIONAL INEQUALITY;

FUNCTIONS;

EID: 0242653626     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026050425030     Document Type: Article

References (22)

1. Auslender, A. (1976) Optimization. Methodes Numeriques, Masson, Paris.
2. Bank, B., Guddat, J., Klatte, D., Kummer, B., and Tammer, K. (1983) Nonlinear Parametric Optimization. Birkhauser Verlag.
3. Blum, E. and Oettli, W. (1993) From optimization and variational inequalities to equilibrium problems. The Mathematics Student 63, 1-23.
4. Cohen, G. (1988) Auxiliary problem principle extended to variational inequalities, Journal of Optimization Theory and Applications 59, 325-333.
5. Ekeland, I. and Temam, R. (1977) Convex analysis and variational problems, North-Holland, Amsterdam.
6. Flam, D.S. and Antipin, A.S. (1997) Equilibrium programming using proximal-like algorithms. Mathematical Programming 78, 29-41.
7. Fukushima, M. (1992) Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems. Mathematical Programming 53, 99-110.
8. Giannessi, F. (1998) On minty variational principle. In New Trends in Mathematical Programming, F. Giannessi, S. Komlosi, and T. Rapcsak, (eds.), Kluwer Academic Publishers, Dordrecht, pp. 93-99.
9. Giannessi, F. (1995) Separation of sets and Gap Functions for Quasi-Variational Inequalities. In Variational Inequalities and Network Equilibrium Problems, F. Giannessi and A. Maugeri, eds., Plenum Publishing Co, 101-121.
10. Giannessi, F., Vector variational inequalities and vector equilibria. Kluwer Academic Publishers, Dordrecht, Boston, London, (2000).
11. Harker, P.T. and Pang, J.S. (1990) Finite-dimensional variational inequalities and nonlinear complementarity problem: a Survey of Theory, Algorithms and Applications. Mathematical Programming 48, 161-220.
12. Karamardian, S. (1976) An existence theorem for the complementary problem. Journal of Optimization Theory and Applications 18, 445-454.
13. Mastroeni, G. (1999) Minimax and extremum problems associated to a Variational Inequality. Supplemento ai Rendiconti del Circolo Matematico di Palermo 58, 185-196.
14. Mastroeni, G. (2000) On auxiliary principle for equilibrium problems. Technical Report of the Department of Mathematics of Pisa University, Italy 3.244.1258, (to appear).
15. Minoux, M. (1986) Mathematical Programming, Theory and Algorithms. John Wiley, New York.
16. Minty, G.J. (1962) Monotone (non linear) operators in Hilbert space. Duke Math. Journal 29, 341-346.
17. Moudafi A. (1999) Proximal point algorithm extended to equilibrium problems, Journal of Natural Geometry 15, 91-100.
18. Ortega, J.M. and Rheinboldt, W.C. (1970) Iterative Solutions of Nonlinear Equations in Everal Variables. Academic Press, New York.
19. Ponstein, J. (1967) Seven kind of convexity. SIAM Rev. 9, 115-119.
20. Yamashita, N., Taji, K. and Fukushima, M. (1997) Unconstrained optimization reformulations of variational inequality problems. Journal of Optimization Theory and Applications 92, 439-456.
21. Zangwill, W.I. (1969) Nonlinear Programming: a unified approach. Prentice-Hall, Englewood Cliffs, NY.
22. Zhu, D.L. and Marcotte, P. (1994) An extended descent framework for variational inequalities Journal of Optimization Theory and Applications 80, 349-366.