上图收敛光滑及其在凸复合函数上的应用
Epi-convergent Smoothing with Applications to Convex Composite Functions
摘要：
平滑方法已经成为研究和解决不可微和约束最优化问题以及一系列其他变分和平衡问题的标准工具集的一部分。本文综合和推广了Beck和Teboulle关于凸函数的下确界卷积光滑的最新结果。关于非凸函数的梯度相容性。我们使用epi收敛技术来定义epi平滑的概念，使我们能够利用丰富的变分结构的次微分非光滑，非凸，非有限值函数。作为一个例子的多功能性和范围epi平滑技术，结果被施加到一般的约束优化，其中非线性规划是一个特例。
英文摘要：
Smoothing methods have become part of the standard tool set for the study and solution of nondifferentiable and constrained optimization problems as well as a range of other variational and equilibrium problems. In this note we synthesize and extend recent results due to Beck and Teboulle on infimal convolution smoothing for convex functions with those of X. Chen on gradient consistency for nonconvex functions. We use epi-convergence techniques to define a notion of epi-smoothing that allows us to tap into the rich variational structure of the subdifferential calculus for nonsmooth, nonconvex, and nonfinite-valued functions. As an illustration of the versatility and range of epi-smoothing techniques, the results are applied to the general constrained optimization for which nonlinear programming is a special case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
