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Keywords:
linear programming; primal-dual interior point methods; kernel functions; complexity analysis; large- and small-update methods
linear programming; primal-dual interior point methods; kernel functions; complexity analysis; large- and small-update methods
Summary:
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 $\mu$-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 kernel function that bridges the gap between the iteration bounds for large-update and small-update methods. To the best of our knowledge, we are the first to achieve these results.
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