An efficient symmetric primal-dual algorithmic framework for saddle point problems

In this paper, we propose a new primal-dual algorithmic framework for a class of convex-concave saddle point problems frequently arising from image processing and machine learning. Our algorithmic framework updates the primal variable between the twice calculations of the dual variable, thereby appearing a symmetric iterative scheme, which is accordingly called the {\bf s}ymmetric {\bf p}r{\bf i}mal-{\bf d}ual {\bf a}lgorithm (SPIDA). It is noteworthy that the subproblems of our SPIDA are equipped with Bregman proximal regularization terms, which make SPIDA versatile in the sense that it enjoys an algorithmic framework covering some existing algorithms such as the classical augmented Lagrangian method (ALM), linearized ALM, and Jacobian splitting algorithms for linearly constrained optimization problems. Besides, our algorithmic framework allows us to derive some customized versions so that SPIDA works as efficiently as possible for structured optimization problems. Theoretically, under some mild conditions, we prove the global convergence of SPIDA and estimate the linear convergence rate under a generalized error bound condition defined by Bregman distance. Finally, a series of numerical experiments on the matrix game, basis pursuit, robust principal component analysis, and image restoration demonstrate that our SPIDA works well on synthetic and real-world datasets.Comment: 32 pages; 5 figure; 7 table

Pseudohexagonal Nb2O5 Anodes for Fast-Charging Potassium-Ion Batteries

High-rate batteries will play a vital role in future energy storage systems, yet while good progress is being made in the development of high-rate lithium-ion batteries, there is less progress with post-lithium-ion chemistry. In this study, we demonstrate that pseudohexagonal Nb2O5(TT-Nb2O5) can offer a high specific capacity (179 mAh g-1 ∼ 0.3C), good lifetime, and an excellent rate performance (72 mAh g-1 at ∼15C) in potassium-ion batteries (KIBs), when it is composited with a highly conductive carbon framework; this is the first reported investigation of TT-Nb2O5 for KIBs. Specifically, multiwalled carbon nanotubes are strongly tethered to Nb2O5 via glucose-derived carbon (Nb2O5@CNT) by a one-step hydrothermal method, which results in highly conductive and porous needle-like structures. This work therefore offers a route for the scalable production of a viable KIB anode material and hence improves the feasibility of fast-charging KIBs for future applications

Pseudohexagonal Nb2O5-Decorated Carbon Nanotubes as a High-Performance Composite Anode for Sodium Ion Batteries

Pseudohexagonal Nb2O5 (TT-Nb2O5) has been applied in sodium ion batteries (SIBs) for the first time. Lower synthesis temperatures, improved conductivity and stability were achieved by the introduction of a designed carbon framework. The TT-Nb2O5/carbon nanotube composite exhibits high specific capacity (135 mAh g−1 at 0.2 A g−1) in long cycles and good rate capability (53 mAh g−1 at high current density of 5 A g−1). The outstanding electrochemical performance is attributed to the superior electrical conductivity and connectivity, optimal mass transport conditions and the mechanical strength and durability established by the strongly linked TT-Nb2O5 and MWCNT network. This study provides a cost-effective route to the application of Nb2O5 in SIBs