Further Development on the Interior Algorithm for Convex Quadratic Programming

The interior trust region algorithm for convex quadratic programming is further developed. This development is motivated by the barrier function and the \center" path-following methods, which create a sequence of primal and dual interior feasible points converging to the optimal solution. At each iteration, the gap between the primal and dual objective values (or the complementary slackness value) is reduced at a global convergence ratio (1 ? 1 4 p n), where n is the number of variables in the convex QP problem. A safeguard line search technique is also developed to relax the small-step-size restriction in the original path-following algorithm.