My research on ADMM dates back to 1997 when I considered the problems from traffic network analysis. Over the last 10 years, the ADMM based on variational inequalities is widely used in optimization. This paper summarizes our research on ADMM over the last 20 years, particularly, the developments in splitting and contraction methods based on ADMM for convex optimization over the last 10 years. We list the main results as well as the motivations. Our analysis is based on the variational inequalities. All methods mentioned fall in a simple unified prediction-correction framework, in which the convergence analysis is quite simple. A through reading will acquaint you with the ADMM, while a more carefully reading may make you familiar with the tricks on constructing splitting methods according to the problem you met. We should notice that the ADMM originates from ALM and PPA, which are good at utilizing the splitting structure. However, it also inherits the intrinsic shortcomings of these first order methods.
Driver scheduling is one of the indispensable core businesses in public transportation system. The driver scheduling problem has attracted much research interests and a large amount of scheduling approaches have been developed since the 1960s. This paper first introduces the driver scheduling problem and its common mathematical model; then, two kinds of solution modes are summarized whilst an overview of driver scheduling approaches are reported; finally, future research trends and directions are suggested.
Blockchain is an important part of the new generation of information technology. It is a new database software integrated with distributed network, encryption technology, smart contract and other technologies. Over the past decade, blockchain technology has had a wide impact on a global scale. Today's blockchain technology has shifted from its initial focus on the decentralization of cryptocurrency and payment to the decentralization of the market. The emergence of smart contract makes the decentralized finance (De-Fi) based on blockchain technology enter a state of rapid development, and various auction scenarios in the context of blockchain also emerge. From the perspective of mechanism design, this paper is the first to summarize and analyze the auction mechanisms on the blockchain in recent years by taking the transaction fee mechanism, NFT auction and MEV auction as the main objects. In addition, we also highlight the challenges and the open problems of the auction mechanism design, based on the characteristics of blockchain.
With the advancement of Internet technology and social network, a multitude of real-world issues can be modeled as combinatorial optimization problems on networks, attracting widespread attention. In the optimization process, agents often engage in strategic behavior driven by personal interests to maximize their utilities. This "selfish" behavior can, on one hand, affect other participants, while on the other hand, the strategies of all agents directly determine the achievement of societal objectives. Therefore, cooperation and competition coexist among participants, giving rise to combinatorial optimization games. This paper aims to delve into three challenging combinatorial optimization games on networks: public goods games, vertex cover games, and routing games. These three categories of games not only hold significant positions in the fields of combinatorial optimization and theoretical computer science, but also have extensive applications across multiple interdisciplinary areas including management science and engineering, economics, and more. To this end, we will provide a systematic introduction to these three types of combinatorial optimization games and thoroughly review their recent research progress and breakthroughs.
