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