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A new algorithm for solving the solution of the linear-quadratic optimizationproblem (LQP) with unseparated boundary conditions in the continuous case isgiven. Using the properties of symmetry of the corresponding Hamiltonianmatrix, the Euler-Lagrange equations, it is shown that linear algebraicequations for determining the missing initial data of the system being solvedhave a symmetric principal matrix. The results are illustrated by the exampleof LQP optimization (stationary case) with minimal control actions.

New sweep algorithm for solving a continuous linear-quadratic optimization problem with unseptable boundary conditions