扰动光滑优化中的锐界
Sharp bounds in perturbed smooth optimization
AI总结：
本文研究扰动凸光滑优化问题，刻画目标函数扰动下解与值的变化，并给出带显式误差项的精确展开。
摘要：
本文研究扰动凸光滑优化问题。主要结果描述了当目标函数受到扰动时，问题的解和值如何变化。例子包括线性、二次和光滑加性扰动。这类问题自然出现在统计学与机器学习、随机优化、稳定性与鲁棒性分析、反问题、最优控制等领域。结果给出了原问题解与其扰动对应问题解之间差异的精确展开，并带有显式误差项。
英文摘要：
This paper studies the problem of perturbed convex and smooth optimization. The main results describe how the solution and the value of the problem change if the objective function is perturbed. Examples include linear, quadratic, and smooth additive perturbations. Such problems naturally arise in statistics and machine learning, stochastic optimization, stability and robustness analysis, inverse problems, optimal control, etc. The results provide accurate expansions for the difference between the solution of the original problem and its perturbed counterpart with an explicit error term.
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。
