未知分段光滑优化的加速近水平方法 II：函数约束优化
Accelerated Prox-Level Methods for Unknown Piecewise-Smooth Optimization II: Function-constrained Optimization
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中文总结 AI 辅助
本文提出重启式惩罚APEX算法，用于求解未知分段光滑的凸函数约束优化问题，该算法可在无需知晓增长模或精确惩罚系数的情况下达到最优预言复杂度，还能生成界定最优性间隙与约束违反量的新可验证证书。
中文摘要 AI 辅助
我们提出一种适用于凸函数约束优化的任意时刻、几乎无参数的算法，其中目标函数和约束函数均为未知分段光滑。该算法为重启式惩罚APEX（探索分段光滑性的加速近水平惩罚方法），是基于惩罚方法的加速束级方法。对于满足二次增长的问题，所提方法是首个无需知晓增长模或精确惩罚系数即可达到最优预言复杂度的方法。此外，重启式惩罚APEX生成可验证的证书，该证书同时界定最优性间隙与约束违反量，且此证书在现有文献中似属首次出现。
英文摘要
We introduce an anytime, almost parameter-free algorithm for convex function-constrained optimization, in which the objective and constraint functions are unknown piecewise-smooth. Our algorithm, Restarted Penalty APEX (Penalty Accelerated Prox-level method for Exploring Piecewise Smoothness), is an accelerated bundle-level method based on the penalty approach. For problems satisfying quadratic growth, the proposed method is the first to achieve optimal oracle complexity without knowing the growth modulus or the exact penalty coefficient. Furthermore, Restarted Penalty APEX generates a verifiable certificate that bounds both the optimality gap and the constraint violation. This certificate also appears to be new to the literature.
发表机构
- Purdue University（普渡大学）
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