A modified simplex embedding method for solving convex optimization problems with a large amount of constraints

A simplex embedding method adapted for solving convex optimization problems with a large amount of constraints is considered. Two modifications of the method are proposed for better performance. First of them uses a more economical approach to the residual computation for constraints, which allows one to significantly reduce the execution time of the algorithm in the case of a large amount of constraints. One of the important peculiarities of the simplex embedding method is its ability to find inactive constraints. This property of the method is used as the basis for its second modification. The numerical results obtained when solving a number of quadratic and convex nondifferentiable optimization problems show the efficiency of the proposed modifications.