Adaptive Linearized Alternating Direction Method of Multipliers for Non-Convex Compositely Regularized Optimization Problems

We consider a wide range of non-convex regularized minimization problems, where the non-convex regularization term is composite with a linear function engaged in sparse learning. Recent theoretical investigations have demonstrated their superiority over their convex counterparts. The computational challenge lies in the fact that the proximal mapping associated with non-convex regularization is not easily obtained due to the imposed linear composition. Fortunately, the problem structure allows one to introduce an auxiliary variable and reformulate it as an optimization problem with linear constraints, which can be solved using the Linearized Alternating Direction Method of Multipliers （LADMM）. Despite the success of LADMM in practice, it remains unknown whether LADMM is convergent in solving such non-convex compositely regularized optimizations. In this research, we first present a detailed convergence analysis of the LADMM algorithm for solving a non-convex compositely regularized optimization problem with a large class of non-convex penalties. Furthermore, we propose an Adaptive LADMM （AdaLADMM） algorithm with a line-search criterion. Experimental results on different genres of datasets validate the efficacy of the proposed algorithm.

The viability of using gasoline-integrated biodiesel-diesel mixtures in engines as a solution to greenhouse gas emissions:a review

The implementation of alternative fuels,such as biodiesel,in engines has been shown to be a feasible strategy to control greenhouse gas(GHG)emissions.The blending of biodiesel with diesel can reduce emissions of carbon monoxide(CO)and carbon dioxide and reduce soot formation.Nonetheless,biodiesel combustion comes with low thermal efficiency,elevated emissions of nitrogen oxides(NOx)and carbon deposition issues.Recently,the addition of gasoline to diesel-biodiesel blends has been proposed to compensate for the downsides of biodiesel combustion.In the current review,the viability of using this ternary fuel blend in engines is thoroughly reviewed.The review first assesses the environmental and health issues caused by conventional fuels,mitigation schemes to control GHG emissions and alternative fuels as a decarbonizing technology.The combustion and emissions characteristics of diesel-bio-diesel-gasoline mixtures are discussed in detail.Finally,the status,challenges and prospects of applying the alternative fuel mixture in engines are appraised.This work has revealed that the mixing of gasoline with diesel-biodiesel blends brings about elongated ignition delay,increased heat release rate and in-cylinder pressure at high loads.Additionally,by adding gasoline,the combustion duration is shortened and soot,CO and unburned hydrocarbon emissions are suppressed,while NOx emissions are slightly increased.Combustion stability is found to be partially disrupted in the presence of gasoline whereas fuel economy(at medium and high loads)is improved by the addition of gasoline.To support the wider deployment and commercialization of this fuelling strategy in the transportation sector,favourable legislation and/or fiscal incentives are needed in countries around the world.This would encourage researchers,fuel producers and engine manufacturers alike to solve challenges such as biodiesel feedstock costs,fuel quality,fuel storage management and engine warranty issues.