Finite-Time Convergent Algorithms for Time-Varying Distributed Optimization

This paper focuses on finite-time (FT) convergent distributed algorithms for solving time-varying distributed optimization (TVDO). The objective is to minimize the sum of local time-varying cost functions subject to the possible time-varying constraints by the coordination of multiple agents in finite time. We first provide a unified approach for designing finite/fixed-time convergent algorithms to solve centralized time-varying optimization, where an auxiliary dynamics is introduced to achieve prescribed performance. Then, two classes of TVDO are investigated included unconstrained distributed consensus optimization and distributed optimal resource allocation problems (DORAP) with both time-varying cost functions and coupled equation constraints. For the previous one, based on nonsmooth analysis, a continuous-time distributed discontinuous dynamics with FT convergence is proposed based on an extended zero-gradient-sum method with a local auxiliary subsystem. Different from the existing methods, the proposed algorithm does not require the initial state of each agent to be the optimizer of the local cost function. Moreover, the provided algorithm has a simpler structure without estimating the global information and can be used for TVDO with nonidentical Hessians. Then, an FT convergent distributed dynamics is further obtained for time-varying DORAP by dual transformation. Particularly, the inverse of Hessians is not required from a dual perspective, which reduces the computation complexity significantly. Finally, two numerical examples are conducted to verify the proposed algorithms

DISA: A Dual Inexact Splitting Algorithm for Distributed Convex Composite Optimization

In this paper, we propose a novel Dual Inexact Splitting Algorithm (DISA) for distributed convex composite optimization problems, where the local loss function consists of a smooth term and a possibly nonsmooth term composed with a linear mapping. DISA, for the first time, eliminates the dependence of the convergent step-size range on the Euclidean norm of the linear mapping, while inheriting the advantages of the classic Primal-Dual Proximal Splitting Algorithm (PD-PSA): simple structure and easy implementation. This indicates that DISA can be executed without prior knowledge of the norm, and tiny step-sizes can be avoided when the norm is large. Additionally, we prove sublinear and linear convergence rates of DISA under general convexity and metric subregularity, respectively. Moreover, we provide a variant of DISA with approximate proximal mapping and prove its global convergence and sublinear convergence rate. Numerical experiments corroborate our theoretical analyses and demonstrate a significant acceleration of DISA compared to existing PD-PSAs

Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach

The accelerated method in solving optimization problems has always been an absorbing topic. Based on the fixed-time (FxT) stability of nonlinear dynamical systems, we provide a unified approach for designing FxT gradient flows (FxTGFs). First, a general class of nonlinear functions in designing FxTGFs is provided. A unified method for designing first-order FxTGFs is shown under PolyakL jasiewicz inequality assumption, a weaker condition than strong convexity. When there exist both bounded and vanishing disturbances in the gradient flow, a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented. Under the strict convexity assumption, Newton-based FxTGFs is given and further extended to solve time-varying optimization. Besides, the proposed FxTGFs are further used for solving equation-constrained optimization. Moreover, an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization. To show the effectiveness of various FxTGFs, the static regret analysis for several typical FxTGFs are also provided in detail. Finally, the proposed FxTGFs are applied to solve two network problems, i.e., the network consensus problem and solving a system linear equations, respectively, from the respective of optimization. Particularly, by choosing component-wisely sign-preserving functions, these problems can be solved in a distributed way, which extends the existing results. The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications

Structure, Mechanical and Electrochemical Properties of Thermally Reduced Graphene Oxide-poly (Vinyl Alcohol) Foams

Graphene oxide foams with a wide range of poly (vinyl alcohol) contents were synthesized by freeze casting, and then thermally reduced at 300ºC in argon atmosphere. Their thermal stability, microstructure, composition and chemical states of constituents, mechanical and electrical properties were investigated by X-ray diffraction, scanning electron microscopy, X-ray photoelectron spectroscopy, thermogravimetry, compressive testing and electrochemical analysis. The results indicated that the PVA content highly influenced the crystallinity and microstructure, resulting in different mechanical properties. After thermal reduction, not only graphene oxide was reduced to graphene, but also PVA was subjected to partial pyrolysis. With the increase of the PVA content, the intensity of the sp2 C-C bond decreased while the sp3 C-C bond increased. Although the mechanical properties decreased after thermal reduction, the composite foams still showed high cyclic structure stability up to 18 % compression strain. Meanwhile, the reduced foams exhibited high electrical conductivity. Applying as anodes in lithium ion battery, the initial discharge capacity for the foams can reach 1822 mA h g-1 and it remained more than 330 mA h g-1 after 50 cycles

Vanadium (V) bio-detoxification based on washing water of rice as microbial and carbon sources

Mining and smelting result in vanadium (V) being released into the environment. Biologically removing V(V) with washing water of rice (WWR) was investigated in this study. Over a 7-d trial, the V(V) removal efficiency increased with dosing washing water of rice dosage up to 56.6%. The results demonstrated that washing water of rice could be used as carbon and microbial sources for biologically reducing V(V). Using domesticated sludge as the inoculum could enhance V(V) detoxification performance, and 95.5% of V(V) was removed in the inoculated system for 5 d. Soluble V(V) was transformed into insoluble V(IV) (VO2), which could be further removed with precipitation. In addition to ABC transporters, a two-component system was also involved in V(V) reduction. The study confirmed that washing water of rice could be utilized for V(V) bio-detoxification

Performance Analysis of OFDM 60GHz System and SC-FDE 60GHz System

In this paper, the performance of 60GHz wireless communication system with SC and OFDM is studied, the models of OFDM 60GHz system and SC 60GHz frequency domain equalization (SC-FDE) system are established, and the bit error rate (BER) performance of OFDM 60GHz system and SC-FDE 60GHz system in 802.15.3c channels is compared. The simulation results show that SC-FDE 60GHz system has a slight advantage over OFDM system in line-of-sight (LOS) channels, while OFDM 60GHz system has a slight advantage over SC-FDE system in non-line-of-sight (NLOS) channels. For 60GHz system, OFDM 60GHz system has a slight advantage over SC-FDE system in overcoming multipath fading, but the performance of both is close whether in the LOS or NLOS case