Abstract
We observe how many equilibrium problems obey a generalized complementarity condition, which in general leads to a variational inequality. We illustrate this fact, by studying the elastic–plastic torsion problem and finding the related Lagrange multipliers.
Similar content being viewed by others
References
Borwein, J.M. and Lewis, A.S. (1989), Practical conditions for Fenchel duality in Infinite Dimensions, Pitman Research Notes in Mathematics Series 252, 83–89.
Brezis, H. and Stampacchia, G. (1968), Sur la regularité de la solution d'inéquations elliptiques, Bull. Soc. Math. Fr. 96, 153–180.
Brezis, H. and Sibony, M. (1971), Equivalence de Deux Inèquations Variationnelles et Applications, Arch. Rational Mech. Anal. 41, 254–265.
Brezis, H. (1972), Multiplicateur de Lagrange en Torsion Elastic—Plastic, Arch. Rational Mech. Anal. 49, 32–40.
Chiadò-Piat, V. and Percivale, D. (1994), Generalized Lagrange multipliers in elastoplastic torsion, Journal of Differential Equations 114, 570–579.
Daniele, P. (1999), Lagrangean function for dynamic variational inequalities, Rendiconti del Circolo Matematico di Palermo Serie II 58, 101–119.
Daniele, P., Maugeri, A. and Oettli, W. (1999), Time-dependent traffic equilibria, J. Opt. Theory Appl., 103, 543–555.
Giannessi, F., Maugeri, A. and Pardalos, P. (2001), Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models, Kluwer Academic Publishers, Dordrecht.
Idone, G., Maugeri, A. and Vitanza, C., Variational Inequalities and the Elastic-Plastic Torsion Problem, J. Opt. Theory Appl., to appear.
Idone, G. and Maugeri, A., Equilibrium problems. In: Qi, Teo and Yang (eds.), Optimization and Control with Applications, Kluwer Academic Publishers, Dordrecht, to appear.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Idone, G., Maugeri, A. & Vitanza, C. Topics on Variational Analysis and Applications to Equilibrium Problems. Journal of Global Optimization 28, 339–346 (2004). https://doi.org/10.1023/B:JOGO.0000026453.62250.61
Issue Date:
DOI: https://doi.org/10.1023/B:JOGO.0000026453.62250.61