论文标题
具有最佳参数函数的时变优化的一类新的路径遵循方法
A New Class of Path-Following Method for Time-Varying Optimization with Optimal Parametric Function
论文作者
论文摘要
在本文中，我们考虑了非线性约束优化问题的公式。 我们使用连续时间参数函数将其重新制定为随着时间变化的优化 并得出一个动态系统，用于跟踪最佳解决方案。 然后，我们将动力学系统重新分配为基于参数函数的线性组合表达它。 变异的计算用于优化参数函数， 使溶液的最佳距离最小化。 因此，一种迭代动态算法，称为op-tvo， 设计以找到有效收敛速率的溶液。 我们使用预测校正方法（PCM）基准了提出的算法的性能 从最优性和计算复杂性观看点。 结果表明，Op-Tvo可以与PCM竞争 为了优化感兴趣的问题， 这表明这可能是一种有前途的方法，可以在某些时变优化问题中替换PCM。 此外，这项工作为解决参数动力学系统提供了一种新颖的范式。
In this paper, we consider a formulation of nonlinear constrained optimization problems. We reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal solution. We then re-parameterize the dynamical system to express it based on a linear combination of the parametric functions. Calculus of variations is applied to optimize the parametric functions, so that the optimality distance of the solution is minimized. Accordingly, an iterative dynamic algorithm, named as OP-TVO, is devised to find the solution with an efficient convergence rate. We benchmark the performance of the proposed algorithm with the prediction-correction method (PCM) from the optimality and computational complexity point-of-views. The results show that OP-TVO can compete with PCM for the optimization problem of interest, which indicates it can be a promising approach to replace PCM for some time-varying optimization problems. Furthermore, this work provides a novel paradigm for solving parametric dynamical system.
