Proximal Gradient-Type Algorithms for a Class of Bilevel Programming Problems

Dan Li, Shuang Chen, Liping Pang
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Abstract

A class of proximal gradient-type algorithm for bilevel nonlinear nondifferentiable programming problems with smooth substructure is developed in this paper. The original problem is approximately reformulated by explicit slow control technique to a parameterized family function which makes full use of the information of smoothness. At each iteration, we only need to calculate one proximal point analytically or with low computational cost. We prove that the accumulation iterations generated by the algorithms are solutions of the original problem. Moreover, some results of complexity of the algorithms are presented in convergence analysis. Numerical experiments are implemented to verify the efficiency of the proximal gradient algorithms for solving this kind of bilevel programming problems.
一类双层规划问题的邻域梯度型算法
本文研究了一类具有光滑子结构的二阶非线性不可微规划问题的近端梯度型算法。利用显式慢速控制技术将原问题近似地转化为充分利用平滑信息的参数化族函数。在每次迭代中,我们只需要解析地计算一个近点或计算成本低。证明了算法产生的累积迭代是原问题的解。在收敛性分析中给出了算法复杂度的一些结果。通过数值实验验证了近端梯度算法求解这类双层规划问题的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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