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An inexact primal-dual algorithm for semi-infinite programming
Mathematical Methods of Operations Research ( IF 0.9 ) Pub Date : 2020-01-01 , DOI: 10.1007/s00186-019-00698-2
Bo Wei , William B. Haskell , Sixiang Zhao

This paper considers an inexact primal-dual algorithm for semi-infinite programming (SIP) for which it provides general error bounds. We create a new prox function for nonnegative measures for the dual update, and it turns out to be a generalization of the Kullback-Leibler divergence. We show that, with a tolerance for small errors (approximation and regularization error), this algorithm achieves an \({\mathcal {O}}(1/\sqrt{K})\) rate of convergence in terms of the optimality gap and constraint violation, where K is the total number of iterations. We then use our general error bounds to analyze the convergence and sample complexity of a specific primal-dual SIP algorithm based on Monte Carlo sampling. Finally, we provide numerical experiments to demonstrate the performance of this algorithm.

中文翻译:

半无限编程的不精确本原对偶算法

本文考虑了一种用于半无限编程(SIP)的不精确的原始对偶算法,该算法为其提供了一般的误差范围。我们为双重更新的非负度量创建了一个新的代理函数,结果证明是Kullback-Leibler散度的推广。我们证明,在容许小的误差(逼近度和正则化误差)的情况下,该算法在最优间隙方面实现了\({\ mathcal {O}}(1 / \ sqrt {K})\)收敛速度和约束违反,其中K是迭代的总数。然后,我们使用通用误差范围来分析基于蒙特卡洛采样的特定原始对偶SIP算法的收敛性和样本复杂度。最后,我们提供了数值实验来证明该算法的性能。
更新日期:2020-01-01
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