【摘要】：研究多個(gè)體網(wǎng)絡(luò)中所有個(gè)體目標(biāo)函數(shù)之和最小值問題,其中每個(gè)個(gè)體僅知其自身目標(biāo)函數(shù)且僅可與其鄰居個(gè)體交互信息。鑒于個(gè)體目標(biāo)函數(shù)通常非光滑,同時(shí)個(gè)體間單變量信息通信有一定局限性,本文提出一種分布式流言push-sum無梯度算法求解此優(yōu)化問題。假設(shè)每個(gè)個(gè)體都具有一個(gè)服從泊松分布的控制時(shí)鐘,時(shí)鐘的每次轉(zhuǎn)動(dòng)表示隨機(jī)選擇的個(gè)體之間進(jìn)行信息更新。進(jìn)一步地,在網(wǎng)絡(luò)連通條件下證明了所提算法的收斂性。數(shù)值仿真結(jié)果表明,與現(xiàn)有的分布式流言無梯度優(yōu)化算法相比,本文算法具有更快的收斂速度。
[Abstract]:In this paper, we study the minimum value of the sum of all individual objective functions in a multi-agent network, where each individual only knows its own objective function and can only interact with its neighbors. In view of the fact that the individual objective function is usually non-smooth and the single variable information communication between individuals has some limitations, this paper presents a distributed gossip push-sum algorithm without gradient to solve this optimization problem. Assuming that each individual has a control clock with a Poisson distribution, each rotation of the clock represents the updating of information between randomly selected individuals. Furthermore, the convergence of the proposed algorithm is proved under the condition of network connectivity. The numerical simulation results show that the proposed algorithm has a faster convergence speed than the existing distributed gossip without gradient optimization algorithm.
【作者單位】： 安徽理工大學(xué)數(shù)學(xué)與大數(shù)據(jù)學(xué)院;
【基金】：國(guó)家自然科學(xué)基金資助項(xiàng)目(61472003) 高校學(xué)科(專業(yè))拔尖人才學(xué)術(shù)資助重點(diǎn)項(xiàng)目(gxbjZD2016049) 安徽省學(xué)術(shù)和技術(shù)帶頭人及后備人選科研活動(dòng)經(jīng)費(fèi)資助項(xiàng)目(2016H076)
【分類號(hào)】：TP18

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