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This paper considers the problem of online optimization where the objective function is time-varying. In particular, we extend coordinate descent type algorithms to the online case, where the objective function varies after a finite number of iterations of the algorithm. Instead of solving the problem exactly at each time step, we only apply a finite number of iterations at each time step. Commonly used notions of regret are used to measure the performance of the online algorithm. Moreover, coordinate descent algorithms with different updating rules are considered, including both deterministic and stochastic rules that are developed in the literature of classical offline optimization. A thorough regret analysis is given for each case. Finally, numerical simulations are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Space-division multiplexed elastic optical networks (SDM-EONs) utilizing multi-core fiber (MCF) have been considered to address the growing traffic demand in transport networks. The quality of transmission (QoT) of MCF-based SDM-EONs is affected by inter-core and intra-core physical layer impairments (PLIs). This paper proposes an inter-core crosstalk-aware and intra-core impairment-aware algorithm for modulation, core, and spectrum assignment (CIA-MCSA) in MCF-based SDM-EONs. The CIA-MCSA considers PLI estimation in a dynamic traffic scenario and allocates new lightpaths using strategies to avoid blocking by insufficient QoT of the new lightpath and of already active lightpaths. Using numerical simulation, the performance of the CIA-MCSA is compared with five algorithms proposed by other authors, considering two distinct network topologies, heterogeneous traffic demands, and different levels of inter-core crosstalk. The results show that, when compared with the most competitive of the other algorithms, (i) CIA-MCSA achieves an average reduction of the request blocking probability by at least 33.87%; (i i) CIA-MCSA achieves an average reduction of the bandwidth blocking probability by at least 20.74%; and (i i i) CIA-MCSA increases the network spectrum utilization by at least 3.04%. [ABSTRACT FROM AUTHOR]

In this paper, a randomized parallel algorithm is proposed to solve the distributed optimal consensus problem of multi-agent systems. Involving both the transient response and the final consensus state, the problem is described as a constrained non-separable optimization problem. Inspired by the randomized Jacobi proximal alternating direction method of multipliers, the proposed algorithm makes it possible for only a fraction of agents to solve their private subproblems in parallel at each iteration, which greatly saves computational resources and enhances running efficiency. The convergence analysis of the algorithm gives fully distributed convergence conditions. A trade-off between the convergence speed and resource savings is then obtained, where the convergence rate is estimated to be at least O 1 t . Furthermore, the algorithm can be accelerated to enjoy a convergence rate of O 1 t 2 by adaptively adjusting the auxiliary parameters properly. Numerical simulations demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]