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Iterative processes for solving incorrect convex variational problems

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Abstract

The present paper is concerned with a general approach to the construction and the numerical analysis of stable methods solving semi-infinite convex programs and variational inequalities of elliptical type in case where the considered problems are incorrect. The approach which is based on the application of the PROX-regularization (cf. Martinet, 1970; Ekeland and Temam, 1976; Rockafellar, 1976; Brézis and Lions, 1978; Lemaire, 1988) secures the strong convergence of the minimizing sequence. The possibility of the algorithmical realization is described and depends on the smoothness properties of the solutions.

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Supported by Deutsche Forschungsgemeinschaft under grant Ti 191/1-1.

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Kaplan, A., Tichatschke, R. Iterative processes for solving incorrect convex variational problems. J Glob Optim 3, 243–255 (1993). https://doi.org/10.1007/BF01096742

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Key words

  • Regularization
  • weakly coercive variational inequalities
  • semi-infinite programming problems
  • numerical algorithms for convex programming problems

AMS 1980 subject classification

  • Primary: 65K10
  • Secondary: 49A29