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This article is cited in 2 scientific papers (total in 2 papers)
Pontryagin's Direct Method for Optimization Problems with Differential Inclusion
E. S. Polovinkin Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141701 Russia
Abstract:
We develop Pontryagin's direct variational method, which allows us to obtain necessary conditions in the Mayer extremal problem on a fixed interval under constraints on the trajectories given by a differential inclusion with generally unbounded right-hand side. The established necessary optimality conditions contain the Euler–Lagrange differential inclusion. The results are proved under maximally weak conditions, and very strong statements compared with the known ones are obtained; moreover, admissible velocity sets may be unbounded and nonconvex under a general hypothesis that the right-hand side of the differential inclusion is pseudo-Lipschitz. In the statements, we refine conditions on the Euler–Lagrange differential inclusion, in which neither the Clarke normal cone nor the limiting normal cone is used, as is common in the works of other authors. We also give an example demonstrating the efficiency of the results obtained.
Keywords:
variational differential inclusion, adjoint Euler–Lagrange differential inclusion, necessary optimality conditions, tangent cones, derivatives of a multivalued mapping, pseudo-Lipschitz condition.
Received: November 18, 2018 Revised: December 19, 2018 Accepted: January 17, 2019
Citation:
E. S. Polovinkin, “Pontryagin's Direct Method for Optimization Problems with Differential Inclusion”, Optimal control and differential equations, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 304, Steklov Math. Inst. RAS, Moscow, 2019, 257–272; Proc. Steklov Inst. Math., 304 (2019), 241–256
Linking options:
https://www.mathnet.ru/eng/tm3983https://doi.org/10.4213/tm3983 https://www.mathnet.ru/eng/tm/v304/p257
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Abstract page: | 315 | Full-text PDF : | 38 | References: | 49 | First page: | 14 |
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