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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DOI: https://doi.org/10.1007/BF01096742
Key words
- Regularization
- weakly coercive variational inequalities
- semi-infinite programming problems
- numerical algorithms for convex programming problems