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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2023, Volume 29, Number 3, Pages 247–260
DOI: https://doi.org/10.21538/0134-4889-2023-29-3-247-260 (Mi timm2029) 		 
Optimization of the Optimal Value Function in Problems of Convex Parametric Programming

O. V. Khamisov

L. A. Melentiev Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences, Irkutsk
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DOI: https://doi.org/10.21538/0134-4889-2023-29-3-247-260
Abstract: We consider a problem of convex parametric programming in which the objective function and the constraint functions are convex functions of an external parameter. Computational procedures are suggested for finding the maximum and minimum values of the optimal value function and for finding inner and outer approximations to the set of parameters for which the problem is consistent. All procedures are based on the application of support functions. Illustrative examples are provided.
Keywords: parametric optimization, optimal value function, support function, inner and outer approximation.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWEU-2021-0006
This work was carried out under the state task project no. FWEU-2021-0006 (registration number АААА-А21-121012090034-3).
Received: 13.06.2023
Revised: 14.08.2023
Accepted: 21.08.2023
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2023, Volume 323, Issue 1, Pages S133–S145
DOI: https://doi.org/10.1134/S0081543823060111
Bibliographic databases:
Document Type: Article
UDC: 519.6
MSC: 28X04
Language: Russian
Citation: O. V. Khamisov, “Optimization of the Optimal Value Function in Problems of Convex Parametric Programming”, Trudy Inst. Mat. i Mekh. UrO RAN, 29, no. 3, 2023, 247–260; Proc. Steklov Inst. Math. (Suppl.), 323, suppl. 1 (2023), S133–S145
Citation in format AMSBIB
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\by O.~V.~Khamisov
\paper Optimization of the Optimal Value Function in Problems of Convex Parametric Programming
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2023
\vol 29
\issue 3
\pages 247--260
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2023
\vol 323
\issue , suppl. 1
\pages S133--S145
\crossref{https://doi.org/10.1134/S0081543823060111}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85185114804}
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