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Purpose: This paper aims to explore the effect of fairness concerns on supply chain members' optimal decisions and profits, to compare their profits under different policies, and to investigate the impact of each policy on members, consumers, and the environment with fairness concerns. Design/methodology/approach: Considering government policies and fairness concerns in recycling management, this paper develops five recycling and remanufacturing decision models (anarchy policy model, reward-penalty mechanism model, recycling investment subsidies model, government tax model, and fund subsidy system model). In each model, the manufacturer and the online platform form the Stackelberg game. This research further discusses comprehensive environmental benefits and consumer surplus under five scenarios. Findings: First, the fairness concerns of the online platform inhibit the recovery rate and supply chain members' profit while increasing the platform's utility. Second, fairness concerns increase the profit gap between the manufacturer and online platform, and the higher the degree of fairness concerns, the greater the profit gap; however, the four policies reduce the profit gap. Finally, when there are fairness concerns, environmental taxes damage the interests of supply chain members and consumers, but are most beneficial to the environment; recycling investment subsidies are on the contrary; the fund subsidy system depends on the relative size of the treatment fund and the subsidy fund. Originality/value: This paper provides useful insights on how to regulate government policy to improve supply chain management with fairness concerns. [ABSTRACT FROM AUTHOR]

Highlights: [•] We solve an open problem proposed in the journal SIAM Review. [•] The problem is about the optimality of an asymptotic solution. [•] We give an affirmative answer to the problem by means of the homotopy analysis method. [Copyright &y& Elsevier]

Weight pruning methods of deep neural networks (DNNs) have been demonstrated to achieve a good model pruning rate without loss of accuracy, thereby alleviating the significant computation/storage requirements of large-scale DNNs. Structured weight pruning methods have been proposed to overcome the limitation of irregular network structure and demonstrated actual GPU acceleration. However, in prior work, the pruning rate (degree of sparsity) and GPU acceleration are limited (to less than 50%) when accuracy needs to be maintained. In this work, we overcome these limitations by proposing a unified, systematic framework of structured weight pruning for DNNs. It is a framework that can be used to induce different types of structured sparsity, such as filterwise, channelwise, and shapewise sparsity, as well as nonstructured sparsity. The proposed framework incorporates stochastic gradient descent (SGD; or ADAM) with alternating direction method of multipliers (ADMM) and can be understood as a dynamic regularization method in which the regularization target is analytically updated in each iteration. Leveraging special characteristics of ADMM, we further propose a progressive, multistep weight pruning framework and a network purification and unused path removal procedure, in order to achieve higher pruning rate without accuracy loss. Without loss of accuracy on the AlexNet model, we achieve $2.58\times $ and $3.65\times $ average measured speedup on two GPUs, clearly outperforming the prior work. The average speedups reach $3.15\times $ and $8.52\times $ when allowing a moderate accuracy loss of 2%. In this case, the model compression for convolutional layers is $15.0\times $ , corresponding to $11.93\times $ measured CPU speedup. As another example, for the ResNet-18 model on the CIFAR-10 data set, we achieve an unprecedented $54.2\times $ structured pruning rate on CONV layers. This is $32\times $ higher pruning rate compared with recent work and can further translate into $7.6\times $ inference time speedup on the Adreno 640 mobile GPU compared with the original, unpruned DNN model. We share our codes and models at the link http://bit.ly/2M0V7DO. [ABSTRACT FROM AUTHOR]

We analyze the learning problem of one-hidden-layer nonoverlapping convolutional neural networks with the rectified linear unit (ReLU) activation function from the perspective of model estimation. The training outputs are assumed to be generated by the neural network with the unknown ground-truth parameters plus some additive noise, and the objective is to estimate the model parameters by minimizing a nonconvex squared loss function of the training data. Assuming that the training set contains a finite number of samples generated from the Gaussian distribution, we prove that the accelerated gradient descent (GD) algorithm with a proper initialization converges to the ground-truth parameters (up to the noise level) with a linear rate even though the learning problem is nonconvex. Moreover, the convergence rate is proved to be faster than the vanilla GD. The initialization can be achieved by the existing tensor initialization method. In contrast to the existing works that assume an infinite number of samples, we theoretically establish the sample complexity of the required number of training samples. Although the neural network considered here is not deep, this is the first work to show that accelerated GD algorithms can find the global optimizer of the nonconvex learning problem of neural networks. This is also the first work that characterizes the sample complexity of gradient-based methods in learning convolutional neural networks with the nonsmooth ReLU activation function. This work also provides the tightest bound so far of the estimation error with respect to the output noise. [ABSTRACT FROM AUTHOR]