High-value utilization of CO_(2) to synthesize sulfur-doped carbon nanofibers with excellent capacitive performance

Carbon nanofiber(CNF)is considered a promising material due to its excellent physical and chemical properties.This paper proposes a novel way to transform CO_(2) into heteroatom-doped CNFs,with the introduction of Fe,Co,and Ni as catalysts.When the electrolyte containing Ni O,Co2O3,and Fe_(2)O_(3) was employed,sulfur-doped CNFs in various diameters were obtained.With the introduction of Fe catalyst,the obtained sulfur-doped CNFs showed the smallest and tightest diameter distributions.The obtained sulfur-doped CNFs had high gravimetric capacitance(achieved by SDG-Fe)that could reach 348.5 F/g at 0.5 A/g,excellent cycling stability,and good rate performance.For comparison purposes,both Fe and nickel cathodes were tested,where the active metal atom at their surface could act as catalyst.In these two situations,sulfur-doped graphite sheet and sulfur-doped graphite quasi-sphere were the main products.

A Bregman-Style Improved ADMM and its Linearized Version in the Nonconvex Setting:Convergence and Rate Analyses

This work explores a family of two-block nonconvex optimization problems subject to linear constraints.We first introduce a simple but universal Bregman-style improved alternating direction method of multipliers(ADMM)based on the iteration framework of ADMM and the Bregman distance.Then,we utilize the smooth performance of one of the components to develop a linearized version of it.Compared to the traditional ADMM,both proposed methods integrate a convex combination strategy into the multiplier update step.For each proposed method,we demonstrate the convergence of the entire iteration sequence to a unique critical point of the augmented Lagrangian function utilizing the powerful Kurdyka–Łojasiewicz property,and we also derive convergence rates for both the sequence of merit function values and the iteration sequence.Finally,some numerical results show that the proposed methods are effective and encouraging for the Lasso model.

A Bregman-style Partially Symmetric Alternating Direction Method of Multipliers for Nonconvex Multi-block Optimization

The alternating direction method of multipliers(ADMM)is one of the most successful and powerful methods for separable minimization optimization.Based on the idea of symmetric ADMM in two-block optimization,we add an updating formula for the Lagrange multiplier without restricting its position for multiblock one.Then,combining with the Bregman distance,in this work,a Bregman-style partially symmetric ADMM is presented for nonconvex multi-block optimization with linear constraints,and the Lagrange multiplier is updated twice with different relaxation factors in the iteration scheme.Under the suitable conditions,the global convergence,strong convergence and convergence rate of the presented method are analyzed and obtained.Finally,some preliminary numerical results are reported to support the correctness of the theoretical assertions,and these show that the presented method is numerically effective.

Convergence of Bregman Peaceman–Rachford Splitting Method for Nonconvex Nonseparable Optimization

This work is about a splitting method for solving a nonconvex nonseparable optimization problem with linear constraints,where the objective function consists of two separable functions and a coupled term.First,based on the ideas from Bregman distance and Peaceman–Rachford splitting method,the Bregman Peaceman–Rachford splitting method with different relaxation factors for the multiplier is proposed.Second,the global and strong convergence of the proposed algorithm are proved under general conditions including the region of the two relaxation factors as well as the crucial Kurdyka–Łojasiewicz property.Third,when the associated Kurdyka–Łojasiewicz property function has a special structure,the sublinear and linear convergence rates of the proposed algorithm are guaranteed.Furthermore,some preliminary numerical results are shown to indicate the effectiveness of the proposed algorithm.