论文标题
不可避免的不可绝非近端交替线性化最小化的收敛特性
The Convergence Properties of Infeasible Inexact Proximal Alternating Linearized Minimization
论文作者
论文摘要
近端交替线性化最小化方法（PALM）非常适合解决块结构的优化问题，这些问题在实际应用中无处不在。在子问题没有封闭式溶液的情况下，例如由于复杂的限制，不可避免的子上落员是必不可少的，因此产生了不可行的不切实际棕榈（Palm-i）。许多努力都致力于分析可行的棕榈，而对棕榈-I的关注很少。因此，棕榈-I的用法缺乏理论保证。分析的基本困难在于由不可行性引起的客观值非单调性。我们在目前的工作中研究棕榈1的收敛特性。特别是，我们构建了一个替代序列来克服非单调性问题并设计了可实现的不精确标准。基于这些，我们设法建立了任何积累点的平稳性，此外，在Lojasiewicz属性的假设下显示了迭代收敛和渐近收敛速率。通过数值实验对量子物理学和3D各向异性摩擦接触引起的问题进行了数值实验，可以说明Palm-I在CPU时间上的显着优势。
The proximal alternating linearized minimization method (PALM) suits well for solving block-structured optimization problems, which are ubiquitous in real applications. In the cases where subproblems do not have closed-form solutions, e.g., due to complex constraints, infeasible subsolvers are indispensable, giving rise to an infeasible inexact PALM (PALM-I). Numerous efforts have been devoted to analyzing feasible PALM, while little attention has been paid to PALM-I. The usage of PALM-I thus lacks theoretical guarantee. The essential difficulty of analyses consists in the objective value nonmonotonicity induced by the infeasibility. We study in the present work the convergence properties of PALM-I. In particular, we construct a surrogate sequence to surmount the nonmonotonicity issue and devise an implementable inexact criterion. Based upon these, we manage to establish the stationarity of any accumulation point and, moreover, show the iterate convergence and the asymptotic convergence rates under the assumption of the Lojasiewicz property. The prominent advantages of PALM-I on CPU time are illustrated via numerical experiments on problems arising from quantum physics and 3D anisotropic frictional contact.
