The kernel functions play an important role in the amelioration of the computational complexity of algorithms. In this paper, we present a primal-dual interior-point algorithm for solving convex quadratic programming based on a new parametric kernel function. The proposed kernel function is not logarithmic and not self-regular. We analysis a large and small-update versions which are based on a new kernel function. We obtain the best known iteration bound for large-update methods, which improves signicantly the so far obtained complexity results. Thisresult is the rst to reach this goal.
In this paper, we deal with the study and implementation of an infeasible interior point method for convex quadratic problems (CQP). The algorithm uses a Newton step and suitable proximity measure for approximately tracing the central path and guarantees that after one feasibility step, the new iterate is feasible and suciently close to the central path. For its complexity analysis, we reconsider the analysis used by the authors for linear optimisation (LO) and linear complementarity problems (LCP).
We show that the algorithm has the best known iteration bound, namely \(n log (n+1)\).
Finally, to measure the numerical performance of this algorithm, it was tested on convex quadratic and linear problems.
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