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Coupling proximal methods and variational convergence

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Abstract

An approximation method which combines a data perturbation by variational convergence with the proximal point algorithm, is presented. Conditions which guarantee convergence, are provided and an application to the partial inverse method is given.

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References

  • Alart P, Lemaire B (1987) Penalization in nonclassical convex programming via variational convergence. To appear in Math. Programming

  • Attouch H, Wets RJB (1991) Quantitative stability of variational systems: I. The epigraphical distance. Trans Amer Math Soc 328, 2:695–729

    Google Scholar 

  • Attouch H, Moudafi A, Riahi H (1991) Quantitative stability analysis for maximal monotone operators and semi-groups of contractions, Seminaire d'Analyse Convexe de Montpellier, Vol. 21

  • Auslender A, Crouzeix JP, Fedit P (1985) Penality-proximal methods in convex programming. To appear in JOTA

  • Lemaire B (1988) Coupling optimization methods and variational convergence. Trends in Mathematical Optimization, International series of Numerical Mathematics, Vol. 84(C), Birkhäuser Verlag, 163–179

  • Luque FJ (1984) Asymptotic convergence analysis of the proximal point algorithm. SIAM J Control and Optimization 22:277–293

    Google Scholar 

  • Martinet B (1972) Algorithmes pour la résolution de problèmes d'optimisation et de minimax. Thèse d'Etat, Université Grenoble

  • Minty GJ (1978) Monotone nonlinear operators in Hilbert space. Duke Math J 2:341–346

    Google Scholar 

  • Mouallif K, Tossings P (1987) Une méthode de pénalisation exponentielle associée à une régularisation proximale. Bull Soc Roy Sc de Liège, 56ème année 2:181–190

    Google Scholar 

  • Moudafi A (1987) Perturbation de la méthode de l'inverse partiel. Publication Avamac 87-05, Université de Perpignan, Vol. II

  • Opial Z (1967) Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull Amer Math Soc 73:591–597

    Google Scholar 

  • Ortega JM, Rheinboldt (1970) Iterative solution of nonlinear equations in several variables. Academic Press, New York

    Google Scholar 

  • Rockafellar RT (1976) Monotone operators and the proximal point algorithm. SIAM J Control and Optimization, 877–898

  • Spingarn JE (1983) Partial inverse of a monotone operator. Appl Math Opt 10:247–265

    Google Scholar 

  • Spingarn JE (1985) Applications of the method of partial inverses to convex programming: decomposition. Math Programming 32:199–223

    Google Scholar 

Download references

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Authors and Affiliations

  1. U.S.T.L. Laboratoire d'Analyse Convexe Département de Mathématiques, Place Eugene Bataillon, 34096, Montpellier, France

    Abdellatif Moudafi

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  1. Abdellatif Moudafi
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Moudafi, A. Coupling proximal methods and variational convergence. ZOR - Methods and Models of Operations Research 38, 269–280 (1993). https://doi.org/10.1007/BF01416609

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  • DOI: https://doi.org/10.1007/BF01416609

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