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Duality methods for solving variational inequalities. (English) Zbl 0456.65036

MSC:
65K10Optimization techniques (numerical methods)
65J15Equations with nonlinear operators (numerical methods)
49J40Variational methods including variational inequalities
47H05Monotone operators (with respect to duality) and generalizations
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References:
[1] A. Bermúdez and C. Moreno, Application of pursuit method to optimal control problems. Appl Math. Opt. (To appear).
[2] Pazy, A.: Semi-groups of nonlinear contractions in Hilbert space. Problems of nonlinear analysis (1971) · Zbl 0228.47038
[3] Hestenes, M. R.: Multiplier and gradient methods. J. opt. Theory appl 4, 303-320 (1969) · Zbl 0174.20705
[4] Powell, M. J. D.: A method for the nonlinear constraints in minimization problems.. Optimization (1972) · Zbl 0254.65047
[5] Glowinski, R.; Marroco, A.: Sur l’approximation par éléments finis d’ordre un, et la résolution par pénalisationdualité, d’une classe de problèmes de Dirichlet non-linéaires. 71-76 (1975) · Zbl 0368.65053
[6] Fortin, M.: Minimization of some non-differential functionals by the augmented Lagrangian method of hestenes and. Powell. appl. Math. opt. 2, No. 3, 236-250 (1976)
[7] Ekeland, I.; Temam, R.: Analyse convexe et inéquations variationnelles. (1974)
[8] Duvaut, G.; Lions, J. L.: LES inéquations en méchanique et en physique. (1972) · Zbl 0298.73001
[9] Glowinski, R.; Lions, J. L.; Tremolieres, R.: Analyse numérique des inéquations variationnelles. (1976) · Zbl 0358.65091
[10] Brezis, H.: Multiplicateur de Lagrange en torsion elastoplastique. Archiv. rat. Mech. anal 49, 32-40 (1972) · Zbl 0265.35021
[11] Pazy, A.: On the asymptotic behaviour of iterates of nonexpasive mappings in Hilbert space. Israel J. Math. 26, 197-204 (1977) · Zbl 0343.47047
[12] Lions, P. L.; Mercier, B.: Splitting algorithms for the sum of two nonlinear operators. Rapport interne no. 29 (1978)
[13] Lions, P. L.: Approximation de points fixes de contractions. CR acad. Sci. Paris ser. A 284, 1357-1358 (1977)
[14] Gabay, D.; Mercier, B.: A dual algorithm for the solution of nonlinerar variational problems via finite element approximation. Comput. math. Appl. 2, 17-40 (1976) · Zbl 0352.65034