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Kernel functions play an important role in designing and analyzing interior-point methods. They are not only used for determining search directions but also for measuring the distance between the given iterate and the -center in the algorithms. Currently, interior-point methods based on kernel functions are among the most effective methods for solving different types of optimization problems and are very active research area in mathematical programming. Therefore, in this work, we introduce a novel...
In this paper, we first present a polynomial-time primal-dual interior-point method (IPM) for solving linear programming (LP) problems, based on a new kernel function (KF) with a hyperbolic-logarithmic barrier term. To improve the iteration bound, we propose a parameterized version of this function. We show that the complexity result meets the currently best iteration bound for large-update methods by choosing a special value of the parameter. Numerical experiments reveal that the new KFs have better...
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