RC Circuits based Distributed Conditional Gradient Method

RLC Circuits based Distributed Mirror Descent Method

We consider distributed optimization with smooth convex objective functions defined on an undirected connected graph. Inspired by mirror descent mehod and RLC circuits, we propose a novel distributed mirror descent method. Compared with mirror-prox method, our algorithm achieves the same \(\mathcal{O}(1/k)\) iteration complexity with only half the computation cost per iteration. We further extend our results to cases where a) gradients are corrupted by stochastic noise, and b) objective function is composed of both smooth and non-smooth terms. We demonstrate our theoretical results via numeric…

Sublinear Circuits and the Constrained Signomial Nonnegativity Problem

Conditional Sums-of-AM/GM-Exponentials (conditional SAGE) is a decomposition method to prove nonnegativity of a signomial or polynomial over some subset $X$ of real space. In this article, we undertake the first structural analysis of conditional SAGE signomials for convex sets $X$. We introduce the $X$-circuits of a finite subset $\mathcal{A} \subset \mathbb{R}^n$, which generalize the simplicial circuits of the affine-linear matroid induced by $\mathcal{A}$ to a constrained setting. The $X$-circuits serve as the main tool in our analysis and exhibit particularly rich combinatorial properties…

Distributed control of reactive power flow in a radial distribution circuit with high photovoltaic penetration

We show how distributed control of reactive power can serve to regulate voltage and minimize resistive losses in a distribution circuit that includes a significant level of photovoltaic (PV) generation. To demonstrate the technique, we consider a radial distribution circuit with a single branch consisting of sequentially-arranged residential-scale loads that consume both real and reactive power. In parallel, some loads also have PV generation capability. We postulate that the inverters associated with each PV system are also capable of limited reactive power generation or consumption, and we s…

时变图上的去中心化条件梯度法

Decentralized conditional gradient method over time-varying graphs

该研究将分布式条件梯度法拓展至时变网络场景，建模时变网络为图随机序列的确定性形式，分析了算法收敛性并给出数值实验验证。

Local Control of Reactive Power by Distributed Photovoltaic Generators

High penetration levels of distributed photovoltaic (PV) generation on an electrical distribution circuit may severely degrade power quality due to voltage sags and swells caused by rapidly varying PV generation during cloud transients coupled with the slow response of existing utility compensation and regulation equipment. Although not permitted under current standards for interconnection of distributed generation, fast-reacting, VAR-capable PV inverters may provide the necessary reactive power injection or consumption to maintain voltage regulation under difficult transient conditions. As si…

分布式优化的等效电路方法

An Equivalent Circuit Approach to Distributed Optimization

受等效电路模型启发提出集中式分布式优化算法ECADO，通过电路聚合灵敏度分析加权与Backward-Euler自适应步长实现快速收敛，在凸及非凸优化问题中迭代次数优于ADMM等先进方法。