New infeasible interior-point algorithm based on monomial method - Yi-Chih, Hsieh; Bricker, Dennis L. (Computers & operations research, 1996)
We propose a new infeasible path-following algorithm for the convex linearly-constrained quadratic programming problem. This algorithm utilizes the monomial method rather than Newton's method for solving the KKT equations at each iteration. As a result, the sequence of iterates generated by this new algorithm is infeasible in the primal and dual linear constraints, but, unlike the sequence of iterates generated by other path-following algorithms, does satisfy the complementarity equations. Performance of this new algorithm is demonstrated by the results of solving QP problems (both separable and nonseparable) which are constructed so as to have known optimal solutions. Additionally, results of solving continuous quadratic knapsack problems indicate that for problems of a given size, the computational time of this new algorithm is less variable than other algorithms.