AI 中文总结
研究非光滑凸泛函不等式约束下的类星体凸优化问题，提出两组含标准和修改变体的算法，通过切换迭代点运行，为确定性和随机设置开发镜像下降型算法并建立收敛速率。
AI 中文摘要
本文考虑受非光滑凸泛函（不等式型）约束的约束优化问题，其中目标函数是非光滑且类星体凸的。我们提出并分析了两组算法，每组由一个标准版本和一个修改变体组成，通过在两种类型的迭代点（有效和无效）之间切换来运行。在每组中，我们为确定性和随机设置开发了不同的镜像下降型算法，并建立了它们的收敛速率。
英文摘要
In this paper, we consider constraint optimization problems subject to non-smooth convex functional (inequality-type) constraints, wherein the objective function is non-smooth and quasar convex. We propose and analyze two groups of algorithms, each consisting of a standard version and a modified variant, that operate by switching between two types of iteration points: productive and non-productive. Within each group, we develop distinct mirror descent-type algorithms for both deterministic and stochastic settings, and we establish their convergence rates.
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