Interior path following primal-dual algorithms. Part II: Convex quadratic programming
Mathematical Programming: Series A and B
Primal-dual interior-point methods
Primal-dual interior-point methods
A New Efficient Large-Update Primal-Dual Interior-Point Method Based on a Finite Barrier
SIAM Journal on Optimization
SIAM Journal on Optimization
SIAM Journal on Optimization
A polynomial-time algorithm for linear optimization based on a new class of kernel functions
Journal of Computational and Applied Mathematics
Steplengths in interior-point algorithms of quadratic programming
Operations Research Letters
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In this paper, we present primal-dual interior-point methods for convex quadratic optimization based on a finite barrier, which has been investigated earlier for the case of linear optimization by Bai et al. (SIAM J Optim 13(3):766---782, 2003). By means of the feature of the finite kernel function, we study the complexity analysis of primal-dual interior-point methods based on the finite barrier and derive the iteration bounds that match the currently best known iteration bounds for large- and small-update methods, namely, $O(\sqrt{n}\log{n}\log{\frac{n}{\varepsilon}})$ and $O(\sqrt{n}\log{\frac{n}{\varepsilon}})$ , respectively, which are as good as the linear optimization analogue. Numerical tests demonstrate the behavior of the algorithms with different parameters.