To improve the convergence speed of distributed online optimization algorithms, a fast first-order Online Distributed Dual Average optimization (FODD) algorithm was proposed by sequentially adding edges to the underlying network topology. Firstly, aiming at solving the problem of the online distributed optimization to make the selected edge and network model mix quickly by using the method of edge addition, a mathematical model was established and solved by FODD. Secondly, the relationship between network topology designed and the convergence rate of the online distributed dual average algorithm was revealed, which clearly showed that, by improving the algebraic connectivity of the underlying topology network, the Regret bound could also be greatly improved. The Online Distributed Dual Average (ODDA) algorithm was extended from static networks to time-varying networks. Meanwhile, the proposed FODD algorithm was proved to be convergent and the convergence rate was specified. Finally, the results of numerical simulations show that, compared with existing algorithms such as ODDA, the proposed FODD algorithm has better convergence performance.

As the existing distributed subgradient optimization algorithms are mainly based on ideal assumptions:the network topology is balanced and the communication among the network is usually the exact information of a state variable of each agent. To relax these assumptions, a distributed subgradient optimization algorithm for switched networks was proposed based on limited quantized information communication. All information along each dynamical edge was quantified by a uniform quantizer with a limited quantization level before being sent in an unbalanced switching network, then the convergence of the multi-agent distributed quantized subgradient optimization algorithm was proved by using non-quadratic Lyapunov function method. Finally, the simulation examples were given to demonstrate the effectiveness of the proposed algorithm. The simulation results show that, under the condition of the same bandwidth, the convergence rate of the proposed optimization algorithm can be improved by adjusting the parameters of the quantizer. Therefore, the proposed optimization algorithm is more suitable for practical applications by weakening the assumptions on the adjacency matrix and the requirement of the network bandwidth.

Concerning that the performance of Mobile Ad Hoc NETwork (MANET) with normal route method degrades obviously when being under attack in battlefield, a new STHR route strategy which integrating AODV（MANET route method） and Spay & Waiter protocols（DTN route method）to achieve high survivability was proposed in this paper. And to reduce the total network load, the method for choosing DTN nodes was designed. At the situation of hard network attacking, the target node may not be searched by AODV search extending ring. Then the zone covering nodes called ZCSEN in this paper would be used to start DTN route progress. In this way, the performance of MANET becomes stable even when it is under attack. The experimental results by 'ONE' show that the delivery rate of STHR is better than AODV and the delay time is shorter than Spay & Waiter route protocol.