An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions
An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions
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DOI：
10.1007/s13675-015-0045-8
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发表时间：
2016-02-01
影响因子：
2.4
通讯作者：
Laszlo, Szilard Csaba
中科院分区：
文献类型：
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作者：
Bot, Radu Ioan;Csetnek, Erno Robert;Laszlo, Szilard Csaba
我们提出了一个向前向后近似型算法的惯性/记忆效应，以最小化的非光滑函数与光滑的非凸设置的总和。由该算法生成的每个迭代序列收敛到目标函数的临界点，只要目标的适当正则化满足Kurdyka-Lojasiewicz不等式，例如对于半代数函数满足该不等式。我们通过两个数值实验来说明理论结果：第一个是关于恢复非凸优化问题的局部最优解的能力，而第二个是关于恢复噪声模糊图像。
We propose a forward-backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. Every sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appropriate regularization of the objective satisfies the Kurdyka-Lojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions. We illustrate the theoretical results by considering two numerical experiments: the first one concerns the ability of recovering the local optimal solutions of nonconvex optimization problems, while the second one refers to the restoration of a noisy blurred image.