We propose a unified framework for time-varying convex optimization based on the prediction-correction paradigm, both in the primal and dual spaces. In this framework, a continuously varying optimization problem is sampled at fixed intervals, and each problem is approximately solved with a primal or dual correction step. The solution method is warm-started with the output of a prediction step, which solves an approximation of a future problem using past information. Prediction approaches are studied and compared under different sets of assumptions. Examples of algorithms covered by this framework are time-varying versions of the gradient method, splitting methods, and the celebrated alternating direction method of multipliers (ADMM).
翻译:我们提议一个基于预测-纠正范式的统一框架,用于在原始空间和双层空间进行时间变化的曲线优化。在这个框架内,对一个不断变化的优化问题进行定期抽样调查,每个问题都大致通过原始或双重修正步骤来解决。 解决办法是用预测步骤的输出来温暖启动,该步骤利用过去的信息解决未来问题的近似值。 预测方法在不同的假设下进行研究和比较。 这一框架所涵盖的算法的例子包括梯度方法的时间变化版本、分裂方法以及备受注意的乘数交替方向方法(ADMM )。