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Lagrange-Hamilton Approach in Optimization Problems with Isoperimetric-Type Constraints

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Abstract

This paper derives necessary optimality conditions for a certain class of optimal control problems without linearity or convexity assumptions. The optimal control problem has a general objective function of integral type and a finite number of isoperimetric type constraints. For proving the main result derived in this paper, the Lagrange function and the control Hamiltonian are introduced and an adjoint differential equation is stated. In addition, we formulate some examples where the derived necessary optimality conditions are applied.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Applied Sciences, University Politehnica of Bucharest, 313 Splaiul Independentei, 060042, Bucharest, Romania

    Savin Treanţă

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  1. Savin Treanţă
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Correspondence to Savin Treanţă.

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Communicated by Jan Sokolowski.

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Treanţă, S. Lagrange-Hamilton Approach in Optimization Problems with Isoperimetric-Type Constraints. J Optim Theory Appl 194, 508–520 (2022). https://doi.org/10.1007/s10957-022-02036-9

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  • DOI: https://doi.org/10.1007/s10957-022-02036-9

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