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In the present paper we studied the problem of nonlinear optimal control of the thermal processes described by Fredholm integro-differential equations when the control parameters are nonlinearly included into the equation as well as into the boundary condition. The concept of weak generalized solution of the boundary value problem is introduced and the algorithm for its construction is indicated. It is established that optimal control is defined as the solution of the system of nonlinear integral equations which contain unknown functions under and out of the integral and satisfy the additional condition in the form of the system of inequalities. Sufficient conditions for the existence of a unique solution of the problem of nonlinear optimization are given, and algorithm of its construction has been developed.

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