Convex Quadratic Minimization Subject to a Linear Constraint and Box Constraints

We consider the problem of minimizing a convex quadratic function over a region defined by a linear equality or inequality constraint and two-sided bounds on the variables (box constraints) in R n . Such problems are interesting from both theoretical and practical points of view because they arise as subproblems of some mathematical programming problems as well as in various practical problems. Polynomial algorithms are proposed for solving problems of this form and their convergence is proved. Some examples and results of numerical experiments are also presented.