Convex two-level optimization problem |
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Authors: | A V Kryazhimskii R A Usachev |
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Institution: | (1) Mathematisches Institut der Universit?t zu K?ln, Weyertal 86-90, 50931 K?ln, Germany |
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Abstract: | A two-level optimization problem is considered in which the objective functional of the second-level problem is minimized
on the solution set of the first-level problem. Convergence of the modified penalty method is established. The main results
include a continuous two-level optimization method based on the regularized extremal shifting principle 3, 5, 6]. For a linearly
convex problem, two-sided bounds on the approximation by the first-level functional are established in addition to convergence.
For a linearly quadratic problem, two-sided bounds on the approximation by the second-level functional are derived. For a
linearly quadratic problem with interval constraints, an explicit form of differential inclusions is presented for the implementation
of the method.
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Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 257–286, 2004. |
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Keywords: | |
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