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Convex two-level optimization problem

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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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Authors
  1. A. V. Kryazhimskii
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  2. R. A. Usachev
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Additional information

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Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 257–286, 2004.

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Kryazhimskii, A.V., Usachev, R.A. Convex two-level optimization problem. Comput Math Model 19, 73–101 (2008). https://doi.org/10.1007/s10598-008-0007-6

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  • DOI: https://doi.org/10.1007/s10598-008-0007-6

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