A proximal method for solving nonlinear minmax location problems with perturbed minimal time functions via conjugate duality
A proximal method for solving nonlinear minmax location problems with perturbed minimal time functions via conjugate duality
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DOI：
10.1007/s10898-019-00746-5
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发表时间：
2019-02
影响因子：
1.8
通讯作者：
S. Grad;O. Wilfer
中科院分区：
文献类型：
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作者：
S. Grad;O. Wilfer
我们通过共轭对偶的方法研究一般的非线性极小极大位置问题，通过一个扩展的扰动最小时间函数，必要和充分的最优性条件，并在某些特殊情况下的最优解的特征一起交付。为了数值求解这类问题，采用了平行分裂邻近点法。我们提出的计算结果在matlabon具体的例子，成功地比较这些，在可能的情况下，与早期类似的方法从文献中。此外，双就业的近端方法原来提供的最佳解决方案所考虑的原始问题的速度比直接使用后者。由于我们的技术成功地解决了高维大数据集的位置优化问题，我们设想其未来用于机器学习中出现的大数据问题。
We investigate via a conjugate duality approach general nonlinear minmax location problems formulated by means of an extended perturbed minimal time function, necessary and sufficient optimality conditions being delivered together with characterizations of the optimal solutions in some particular instances. A parallel splitting proximal point method is employed in order to numerically solve such problems and their duals. We present the computational results obtained inmatlabon concrete examples, successfully comparing these, where possible, with earlier similar methods from the literature. Moreover, the dual employment of the proximal method turns out to deliver the optimal solution to the considered primal problem faster than the direct usage on the latter. Since our technique successfully solves location optimization problems with large data sets in high dimensions, we envision its future usage on big data problems arising in machine learning.