Algorithms For Solving Convex Quadratic Programming With Box Constraints

In this paper, we mainly consider the convex quadratic programming with box constraints. This problem arises in several areas of applications. In Chapter 2, considering the feasible region X = {x|l ≤ x ≤ m, x ∈ R~n} is a simple and special super cuboid. we present a kind of direct interior-point algorithm on X. It reaches the optimal solution by solving a subproblem with super ellipsoid constraints embeded in the super cuboid. We prove that our algorithm is globally convergent. And in Chapter 3, we present a potential-reduction interior-point method for solving this problem. At each step of the algorithm ,a system of linear equation is solved to get a search direction and the Armijo's rule is used to determine a step size. Simultaneously the value of the potential function is reduced. we prove that for any initial point the sequence produced by the algorithm is bounded and every accumulation point of the sequence is the optimal solution of the problem. In other word ,this algorithm has the globalconvergence.