In this paper, we first propose a new finite exponential-trigonometric kernel function that has finite value at the boundary of the feasible region. Then by using some simple analysis tools, we show that the new kernel function has exponential convexity property. We prove that the large-update primal-dual interior-point method based on this kernel function for solving linear optimization problems has \(O\left( \sqrt{n}\log n\log \frac{n}{\epsilon }\right)\) iteration bound in the worst case when the barrier parameter is taken large enough. Moreover, the numerical results reveal that the new finite exponential-trigonometric kernel function has better results than the other kernel functions.

中文翻译：

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基于带有有限指数三角障碍项的新核函数的线性规划问题的有效原对偶内点法

在本文中，我们首先提出了一个新的有限指数三角核函数，该函数在可行区域的边界处具有有限的值。然后通过使用一些简单的分析工具，我们证明了新的核函数具有指数凸性。我们证明基于该内核函数的大更新原始对偶内点法用于解决线性优化问题具有\（O \ left（\ sqrt {n} \ log n \ log \ frac {n} {\ epsilon} \ right）\）在最坏的情况下，如果将barrier参数取得足够大，迭代边界就会变大。此外，数值结果表明，新的有限指数三角核函数比其他核函数具有更好的结果。