The solution of one problem of minimizing a quadratic function using the method of exact penalty

The problem of conditional minimization of quadratic functions with positive definite matrix on the set specified by inequality is considered. For solution of the problem is proposed to use the method of exact penalty functions. Based method that minimizes the penalty function with constant step and have a geometric convergence rate is similar in the smooth case, the gradient method of minimization of convex functions. To find the direction of descent is solved quadratic programming.