Abstract
We show that many equilibrium problems fulfill a common law expressed by a set of complementarity conditions and that the equilibrium solution is obtained as a solution to a Variational Inequality. In particular we show that various models of elastoplastic torsion are included in the framework above.
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References
Borwein, J.M. and Lewis, A.S. (1991), Practical conditions for Fenchel duality in Infinite Dimension, Pitman Research Notes in Mathematics Series, 252, pp. 83–89.
Brézis, H. (1972), Multiplicateur de Lagrange en torsion éasto-plastique, Arch. Rational Mech. Anal., 49, pp. 32–40.
Brézis, H. and Stampacchia, G. (1977), Remarks on some fourth order variational inequality, Ann. Scuola Norm. Sup. Pisa (4), pp. 363–371.
Brézis, H. (1972), Problèmes Unilatéraux, J. Mat. pures et appl. 51, pp. 1–168.
Chiadò, V. and Percivale, D. (1994), Generalized Lagrange Multipliers in Elastoplastic torsion, Journal of Differential Equations, 114, pp. 570–579.
Daniele, P. (1999), Lagrangean function for dynamic Variational Inequalities, Rendiconti del Circolo Matematico di Palermo, 58, pp. 101–119.
Idone, G., Variational inequalities and application to a continuum model of transportation network with capacity constraints, to appear.
Idone, G., Maugeri, A. and Vitanza, C. (2002), Equilibrium problems in Elastic-Palstic Torsion, Boundary Elements 24th, Brebbia C.A., Tadeu A., Popov V. Eds., WIT Press, Southampton, Boston, pp. 611–616.
Lanchon, H. (1969), Solution du problème de torsion élasto-plastique, d'une barre cylindrique de section quelconque, C.R. Acad. Sci. Paris, 269, pp. 791–794.
Maugeri, A. (2001), Equilibrium problems and variational inequalities, in: Equilibrium Problems: nonsmooth optimization and variational inequalities models, Maugeri A., Giannessi F. and Pardalos P. Eds., Kluwer Academic Publishers, pp. 187–205.
Maugeri A. (1998), Dynamic models and generalized equilibrium problems, in: New Trends in Mathematical Programming, Giannessi F. et al. (eds.), Kluwer Academic Publishers, pp. 191–202.
Nagurney A. (1993), Network economics. A Variational Inequality Approach, Kluwer Academic Publishers.
Ting, J.W. (1969), Elasto-plastic torsion of convex cylindrical bars, J. Math. Mech., 19, pp. 531–551.
Troianiello, G.M. (1987), Elliptic Differential Equations and obstacle problems, Plenum Press.
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Idone, G., Maugeri, A. (2005). Equilibrium Problems. In: Qi, L., Teo, K., Yang, X. (eds) Optimization and Control with Applications. Applied Optimization, vol 96. Springer, Boston, MA. https://doi.org/10.1007/0-387-24255-4_26
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DOI: https://doi.org/10.1007/0-387-24255-4_26
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-24254-5
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