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

65K10Optimization techniques (numerical methods)
65J15Equations with nonlinear operators (numerical methods)
49J40Variational methods including variational inequalities
47H05Monotone operators (with respect to duality) and generalizations
Full Text: DOI
[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