Optimization of differential inclusions with parameter

Elimhan N. Mahmudov; Shakir Sh. Yusubov; Dilara I. Mastaliyeva; Elimhan N. Mahmudov; Shakir Sh. Yusubov; Dilara I. Mastaliyeva

doi:10.3934/jimo.2026008

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 1: 214-237. doi: 10.3934/jimo.2026008

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Research article

Optimization of differential inclusions with parameter

1.
Research Center, Azerbaijan National Aviation Academy, Baku, Azerbaijan
2.
Azerbaijan Functional analysis and its applications, Azerbaijan University of Architecture and Construction, Baku, Azerbaijan
3.
Department of Mechanics and Mathematics, Baku State University, Baku, Azerbaijan
4.
Department of Mathematics, Khazar University, Baku, Azerbaijan

Received: 29 April 2025 Revised: 28 September 2025 Accepted: 27 October 2025 Published: 19 November 2025
34A60, 34B08, 34A45, 49K15, 90C90

The article considered the Bolza optimization problem for differential inclusions (DFIs) with a parameter. To achieve the final goal, the corresponding discrete, discrete-approximate, and continuous problems were studied in parallel. Under a standard interior point condition from convex analysis, optimality conditions for the given parameter-dependent problem were obtained in terms of the Euler–Lagrange equations and the Hamiltonian. The central approach relied on the equivalence results of locally adjoint mappings (LAMs). Specifically, a classical optimal control problem with a parameter was investigated.
- Euler-Lagrange,
- parameter,
- differential inclusion,
- Hamiltonian,
- equivalence,
- necessary and sufficient
Citation: Elimhan N. Mahmudov, Shakir Sh. Yusubov, Dilara I. Mastaliyeva. Optimization of differential inclusions with parameter[J]. Journal of Industrial and Management Optimization, 2026, 22(1): 214-237. doi: 10.3934/jimo.2026008

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Abstract

The article considered the Bolza optimization problem for differential inclusions (DFIs) with a parameter. To achieve the final goal, the corresponding discrete, discrete-approximate, and continuous problems were studied in parallel. Under a standard interior point condition from convex analysis, optimality conditions for the given parameter-dependent problem were obtained in terms of the Euler–Lagrange equations and the Hamiltonian. The central approach relied on the equivalence results of locally adjoint mappings (LAMs). Specifically, a classical optimal control problem with a parameter was investigated.

References

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