We propose a communication and computation efficient second-order method for distributed optimization. For each iteration, our method only requires $\mathcal{O}(d)$ communication complexity, where $d$ is the problem dimension. We also provide theoretical analysis to show the proposed method has the similar convergence rate as the classical second-order optimization algorithms. Concretely, our method can find~$\big(\epsilon, \sqrt{dL\epsilon}\,\big)$-second-order stationary points for nonconvex problem by $\mathcal{O}\big(\sqrt{dL}\,\epsilon^{-3/2}\big)$ iterations, where $L$ is the Lipschitz constant of Hessian. Moreover, it enjoys a local superlinear convergence under the strongly-convex assumption. Experiments on both convex and nonconvex problems show that our proposed method performs significantly better than baselines.
Distributed optimization in resource constrained devices demands both communication efficiency and fast convergence rates. Newton-type methods are getting preferable due to their superior convergence rates compared to the first-order methods. In this paper, we study a new problem in regard to the second-order distributed optimization over unreliable networks. The working devices are power-limited or operate in unfavorable wireless channels, experiencing packet losses during their uplink transmission to the server. Our scenario is very common in real-world and leads to instability of classical distributed optimization methods especially the second-order methods because of their sensitivity to the imprecision of local Hessian matrices. To achieve robustness to high packet loss, communication efficiency and fast convergence rates, we propose a novel distributed second-order method, called RED-New (Packet loss Resilient Distributed Approximate Newton). Each iteration of RED-New comprises two rounds of light-weight and lossy transmissions, in which the server aggregates the local information with a new developed scaling strategy. We prove the linear-quadratic convergence rate of RED-New. Experimental results demonstrate its advantage over first-order and second-order baselines, and its tolerance to packet loss rate ranging from 5% to 40%.
The Zhundong coalfield has attracted ever-increasing attention as a result of its super-large reserve of coal resources. However, the power plants encounter great challenges in the utilization of Zhundong coal as a result of its high-alkali feature, which deteriorates the phenomenon of ash deposition and slagging. Oxy-fuel combustion of Zhundong coal benefits the near-zero emission of pollutants in coal-fired power plants, while previous studies mainly focused on the behaviors of alkali and alkaline earth metals and ash deposition during air combustion. The present study focused on the characteristics of ash deposition during oxy-fuel combustion of high-alkali coal, especially the differences in morphologies and chemical compositions of ash deposits using a drop-tube furnace, with the ash deposition mechanisms being further elucidated. Experimental results showed that the contents of sulfur (S), chlorine (Cl), and calcium (Ca) in ash deposits from oxy-fuel combustion were lower at the identical O2 content but the contents of aluminum (Al) and silicon (Si) were increased in comparison to air conditions. The average particle size of ash deposits under oxy-fuel conditions was smaller with less calcium sulfate and mullite than the case in air combustion of Zhundong coal. The adhesion phenomenon between ash particles was aggravated in the ash deposits of high-alkali coal, with the oxygen content elevated. The proportion and diameters of spherical particles declined with an increasing oxygen concentration in the ash deposits of Zhundong coal. The contents of iron (Fe) and calcium in ash deposits of high-alkali coal were closely bound with the decrease of the melting point of ash and the formation of spherical ash particles. The caking phenomenon became more serious as the flue gas temperature was increased in the ash deposits of Zhundong coal. The deposition propensity of Zhundong coal was inclined to the minimum when the probe surface temperature was 550 °C, while the deposition propensity of Lu'an coal was different possibly as a result of the differences in coal properties and ash compositions. During the combustion of high-alkali coals, some components deteriorated ash deposition, including the low-temperature eutectics formed by the reactions of Fe and Ca with Si–Al compounds and sulfates and chlorides of sodium or calcium. This paper is beneficial for the improved understanding of ash deposition during oxy-fuel combustion of high-alkali coal.
With the rapid development of the low-rank coal chemistry industry, the production of semi-coke has ever been increasing.However, the semi-coke is difficult to burnout and the NOx generation during semi-coke combustion is high.Therefore, the co-combustion of semi-coke and bituminous coal in utility boiler is considered as a promising approach to realize the efficient utilization of the semi-coke.Here, the cocombustion features of bituminous coal and semi-coke blends were investigated in a 660 MW utility boiler.The results show that the NOx generation decreases firstly and then increases with the rises of the load and the fraction of semi-coke.The effects of load and blending ratio of semi-coke are both obvious on burnout behavior than those on NOx generation.With the rise of oxygen concentration, the NOx generation rises and the unburned carbon in fly ash decreases.The Na-bearing mineral are better-preserved with the higher oxygen concentration.The experimental results may provide guidance for the realization of the utilization of the semicoke in the utility boiler.
The treatment of antibiotic filter residue (AFR) is an important issue, because of its special nature, the large output, and the difficulty of combustion.Nowadays, the AFR is generally incinerated, but dioxins are produced during the process, which makes incineration technology face challenges.There is a lack of research on the influences of co-combustion conditions on temperature field and flue gas characteristics, but it plays an important role in practical applications.The present study aimed to investigate the influences of AFR mixed with biogas on furnace temperature field and emission characteristics through numerical simulation.The results showed that the opposed injection position was the best type when the proportion of mixed biogas was constant.The results can provide new insight into co-combustion and thermal utilization of AFR.
This paper proposes a novel class of block quasi-Newton methods for convex optimization which we call symmetric rank-$k$ (SR-$k$) methods. Each iteration of SR-$k$ incorporates the curvature information with $k$ Hessian-vector products achieved from the greedy or random strategy. We prove SR-$k$ methods have the local superlinear convergence rate of $\mathcal{O}\big((1-k/d)^{t(t-1)/2}\big)$ for minimizing smooth and strongly self-concordant function, where $d$ is the problem dimension and $t$ is the iteration counter. This is the first explicit superlinear convergence rate for block quasi-Newton methods and it successfully explains why block quasi-Newton methods converge faster than standard quasi-Newton methods in practice.
This paper studies the strongly-convex-strongly-concave minimax optimization with unbalanced dimensionality. Such problems contain several popular applications in data science such as few shot learning and fairness-aware machine learning task. The design of conventional iterative algorithm for minimax optimization typically focuses on reducing the total number of oracle calls, which ignores the unbalanced computational cost for accessing the information from two different variables in minimax. We propose a novel second-order optimization algorithm, called Partial-Quasi-Newton (PQN) method, which takes the advantage of unbalanced structure in the problem to establish the Hessian estimate efficiently. We theoretically prove our PQN method converges to the saddle point faster than existing minimax optimization algorithms. The numerical experiments on real-world applications show the proposed PQN performs significantly better than the state-of-the-art methods.
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