Self-triggered time-varying convex optimization
Self-triggered time-varying convex optimization
复制标题
自触发时变凸优化
DOI：
10.1109/cdc.2016.7798732
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
V. Preciado
中科院分区：
文献类型：
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作者：
Mahyar Fazlyab;Cameron Nowzari;George Pappas;Alejandro Ribeiro;V. Preciado
在本文中，我们提出了一种自触发算法来解决一类具有时变目标函数的凸优化问题。众所周知，最优解的轨迹可以通过连续时间状态更新律渐近跟踪。不幸的是，实现这一点需要连续评估目标函数的梯度和逆 Hessian 矩阵，这不适合数字实现。或者，我们从自触发控制中汲取灵感，提出一种策略，该策略可以自主调整目标函数计算的时间，从而产生分段仿射状态更新定律。该算法通过使用目标函数高阶导数的已知上限来预测梯度的时间演化来实现这一点。我们提出的方法保证在有限时间内收敛到最优轨迹的任意小邻域，并且不会产生芝诺行为。我们通过数值模拟来说明我们的框架。
In this paper, we propose a self-triggered algorithm to solve a class of convex optimization problems with time-varying objective functions. It is known that the trajectory of the optimal solution can be asymptotically tracked by a continuous-time state update law. Unfortunately, implementing this requires continuous evaluation of the gradient and the inverse Hessian of the objective function which is not amenable to digital implementation. Alternatively, we draw inspiration from self-triggered control to propose a strategy that autonomously adapts the times at which it makes computations about the objective function, yielding a piece-wise affine state update law. The algorithm does so by predicting the temporal evolution of the gradient using known upper bounds on higher order derivatives of the objective function. Our proposed method guarantees convergence to arbitrarily small neighborhood of the optimal trajectory in finite time and without incurring Zeno behavior. We illustrate our framework with numerical simulations.