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A proximal point algorithm for control approximation problems

Part I: Theoretical background

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Abstract

We consider the optimization problem

$$f(x): = (c,x) + \sum\limits_{i = 1}^n {\alpha _i \parallel A^i x - a^i \parallel ^{\beta _i } \to \mathop {\min }\limits_{x \in D} ,} $$

which is an extension of a problem studied by Idrissi, Lefebvre and Michelot [7]. This class of problems contains many practically important special cases so as approximation, location and optimal control problems, perturbed linear programming problems and surrogate problems for linear programming. Necessary and sufficient optimality conditions are derived using the sub-differential calculus. A proximal point algorithm is modified by the method of partial inverse [13] in order to solve the optimality conditions.

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Authors and Affiliations

  1. FB Mathematik und Informatik, Institut für Optimierung und Stochastik, Martin-Luther-Universität, 06099, Halle-Wittenberg, Halle, Germany

    H. Benker, A. Hamel & C. Tammer

Authors
  1. H. Benker
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  2. A. Hamel
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  3. C. Tammer
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Benker, H., Hamel, A. & Tammer, C. A proximal point algorithm for control approximation problems. Mathematical Methods of Operations Research 43, 261–280 (1996). https://doi.org/10.1007/BF01194548

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  • DOI: https://doi.org/10.1007/BF01194548

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