Gossip-based distributed stochastic mirror descent for constrained optimization.

This paper considers a distributed constrained optimization problem over a multi-agent network in the non-Euclidean sense. The gossip protocol is adopted to relieve the communication burden, which also adapts to the constantly changing topology of the network. Based on this idea, a gossip-based distributed stochastic mirror descent (GB-DSMD) algorithm is proposed to handle the problem under consideration. The performances of GB-DSMD algorithms with constant and diminishing step sizes are analyzed, respectively. When the step size is constant, the error bound between the optimal function value and the expected function value corresponding to the average iteration output of the algorithm is derived. While for the case of the diminishing step size, it is proved that the output of the algorithm uniformly approaches to the optimal value with probability 1. Finally, as a numerical example, the distributed logistic regression is reported to demonstrate the effectiveness of the GB-DSMD algorithm.

Influence of FexOy and Al2O3 Contents on the Thermal Stability of Iron Ore-Waste Fibers: Key Mechanisms and Control.

Traditional rock wool fibres are susceptible to crystallization and pulverization. To mitigate this, glass fibres were produced from iron ore waste (IOW). When the ratio of Fe2+ and Fe3+ is 1:3 and the Al2O3 content is 10 wt.%, increasing the FexOy content enhances the thermal stability.At an FexOy content of 17-19% and an Al2O3 content of 10-13%, the glass transition temperature (Tg) peaked. Increasing the FexOy content from 10% to 20% enhanced the stability of Si-O and Al-O bonds and increased bridged oxygen, stabilizing the structure. Here, Fe2+ balances structural charges, while Fe3+ replaces some Al atoms in the network. When the Al2O3 content is 10-13% and the FexOy content is 17-19%, the thermal stability of the IOW rock glass reaches its optimal level. At 20% FexOy content, the structure becomes three-dimensional and cyclic, increasing polymerization. Consequently, incorporating FexOy alongside a 10% Al2O3 content improves thermal stability, supporting the development of high-stability rock wool from IOW. This approach also enhances the refractory properties of rock wool fibres within the FexOy-Al2O3-SiO2-MgO-CaO system.