Abstract:
A nonconvex optimal control problem is examined for a system that is linear with respect to state and has a terminal objective functional representable as the difference of two convex functions. A new local search method is proposed, and its convergence is proved. A strategy is also developed for the search of a globally optimal control process, because the Pontryagin and Bellman principles as applied to the above problem do not distinguish between the locally and globally optimal processes. The convergence of this strategy under appropriate conditions is proved.
Key words:
optimal control, locally and globally optimal processes, optimality principles, optimality conditions, global search strategy.
Citation:
A. S. Strekalovskii, M. V. Yanulevich, “Global search in the optimal control problem with a terminal objective functional represented as the difference of two convex functions”, Zh. Vychisl. Mat. Mat. Fiz., 48:7 (2008), 1187–1201; Comput. Math. Math. Phys., 48:7 (2008), 1119–1132
\Bibitem{StrYan08}
\by A.~S.~Strekalovskii, M.~V.~Yanulevich
\paper Global search in the optimal control problem with a~terminal objective functional represented as the difference of two convex functions
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2008
\vol 48
\issue 7
\pages 1187--1201
\mathnet{http://mi.mathnet.ru/zvmmf4559}
\transl
\jour Comput. Math. Math. Phys.
\yr 2008
\vol 48
\issue 7
\pages 1119--1132
\crossref{https://doi.org/10.1134/S0965542508070051}
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Linking options:
https://www.mathnet.ru/eng/zvmmf4559
https://www.mathnet.ru/eng/zvmmf/v48/i7/p1187
This publication is cited in the following 10 articles:
A S Strekalovsky, “On nonconvex optimal control problems”, J. Phys.: Conf. Ser., 1715:1 (2021), 012047
A. S. Strekalovsky, Lecture Notes in Computer Science, 12755, Mathematical Optimization Theory and Operations Research, 2021, 17
Gornov A.Yu., Zarodnyuk T.S., Anikin A.S., Finkelstein E.A., “Extension Technology and Extrema Selections in a Stochastic Multistart Algorithm For Optimal Control Problems”, J. Glob. Optim., 76:3, SI (2020), 533–543
Strekalovsky A.S., Yanulevich M.V., “on Global Search in Nonconvex Optimal Control Problems”, J. Glob. Optim., 65:1, SI (2016), 119–135
Siswanto D., Zhang L., Navaie K., Deepak G.C., “Weighted Sum Throughput Maximization in Heterogeneous Ofdma Networks”, 2016 IEEE 83Rd Vehicular Technology Conference (Vtc Spring), IEEE Vehicular Technology Conference Proceedings, IEEE, 2016
Diky Siswanto, Li Zhang, Keivan Navaie, G. C. Deepak, 2016 IEEE 83rd Vehicular Technology Conference (VTC Spring), 2016, 1
A. S. Strekalovskii, “Sovremennye metody resheniya nevypuklykh zadach optimalnogo upravleniya”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 8 (2014), 141–163
Strekalovsky A.S., “Global Optimality Conditions for Optimal Control Problems with Functions of Ad Alexandrov”, J. Optim. Theory Appl., 159:2 (2013), 297–321
Strekalovsky A.S., Yanulevich M.V., “Global Search in a Noncovex Optimal Control Problem”, J. Comput. Syst. Sci. Int., 52:6 (2013), 893–908
A. S. Strekalovsky, “Maximizing a state convex Lagrange functional in optimal control”, Autom. Remote Control, 73:6 (2012), 949–961
Citation in format AMSBIB
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