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


MSC:

65K10 Numerical optimization and variational techniques
65J15 Numerical solutions to equations with nonlinear operators
49J40 Variational inequalities
47H05 Monotone operators and generalizations
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[1] A. Bermúdez and C. Moreno, Application of pursuit method to optimal control problems. Appl Math. Opt. (To appear).; 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, (Cremonese, Problems of Nonlinear Analysis (1971), C.I.M.E: C.I.M.E Roma) · 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., (Fletcher, R., Optimization (1972), Academic Press: Academic Press New York) · Zbl 0194.47701
[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), RAIRO, R2 · Zbl 0368.65053
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[9] Glowinski, R.; Lions, J. L.; Tremolieres, R., Analyse Numérique des Inéquations variationnelles (1976), Dunod: Dunod Paris · 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), Ecole Polytechnique) · Zbl 0426.65050
[13] Lions, P. L., Approximation de points fixes de contractions, C.R. Acad. Sci. Paris Ser. A, 284, 1357-1358 (1977) · Zbl 0349.47046
[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
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