A continuous conditional gradient method

In this paper we study the continuous conditional gradient method to solve convex minimization problems in Hilbert space. First, sufficient conditions for convergence are provided and the convergence rate is found for a minimization problem with a strong convex function. Then, the regularized method is considered for a minimization problem with inaccurate inital data. Regularization is based on the continuous conditional gradient method in conjunction with the penalty function method. The sufficient conditions for the convergence of the regularized method are presented, the regularizing operator is constructed, and a stopping rule for the continuous process is proposed.