Continuous-Time Algorithm Based on Finite-Time Consensus for Distributed Constrained Convex Optimization

Distributed stochastic projection-free solver for constrained optimization

“…The doubly stochastic adjacent matrix W enables each agent to take a weighted average of its neighbors' information. The doubly stochastic W satisfying |λ 2 (W )| < 1 exists for connected undirected and weight-balanced directed graphs, which are common in the distributed optimization [14], [16], [39]. [23], [35] O [35] O(mn ln(…”

“…One category is primal projected gradient descent algorithms [11]- [13], which are based on the premise that the projection on constraint sets is simple. The second category of algorithms is primal-dual algorithms [14]- [16], which usually involve constructing a dual optimal set containing the dual optimal variable. Furthermore, for large-scale constrained finite-sum optimization, where the calculation of exact local gradients is expensive, some distributed stochastic algorithms estimate the local gradients by sampling data and use projection operators [17]- [19] or primal-dual frameworks [20]- [22] to obtain feasible solutions.…”

Fully distributed containment of multiple‐input‐multiple‐output linear multi‐agent systems with multiple nonautonomous leaders

“…[1][2][3][4][5][6][7] Among many cooperative goals, consensus (synchronization) which seeks to reach an agreement on a common value is the most fundamental goal from which other goals can be achieved. [8][9][10][11][12][13][14] According to whether there exists a leader, consensus is classified into leader-following consensus and leaderless consensus, 15,16 where the former one is much more suitable for real applications since the leader plays a role of generating an ideal goal. While leaders with zero inputs were studied in most existing works which may be unrealistic since the leader may need some inputs for completing specific tasks such as obstacle avoidance.…”

“…Cooperative control of multi‐agent systems (MASs) and cooperative analysis of complex networks have gained a surge of interest over the past decades because of their wide range of applications in many fields such as formation of aircrafts, data fusion, network resource allocation, and so forth 1‐7 . Among many cooperative goals, consensus (synchronization) which seeks to reach an agreement on a common value is the most fundamental goal from which other goals can be achieved 8‐14 …”