A Dynamically Adjusted Subspace Gradient Method and Its Application in Image Restoration

In this paper, a new subspace gradient method is proposed in which the search direction is determined by solving an approximate quadratic model in which a simple symmetric matrix is used to estimate the Hessian matrix in a three-dimensional subspace. The obtained algorithm has the ability to automatically adjust the search direction according to the feedback from experiments. Under some mild assumptions, we use the generalized line search with non-monotonicity to obtain remarkable results, which not only establishes the global convergence of the algorithm for general functions, but also R-linear convergence for uniformly convex functions is further proved. The numerical performance for both the traditional test functions and image restoration problems show that the proposed algorithm is efficient.

A Tristage Adaptive Biased Learning for Artificial Bee Colony

In recent ten years, artificial bee colony (ABC) has attracted more and more attention, and many state-of-the-art ABC variants (ABCs) have been developed by introducing different biased information to the search equations. However, the same biased information is employed in employed bee and onlooker bee phases, which will cause over exploitation and lead to premature convergence. To overcome this limit, an effective framework with tristage adaptive biased learning is proposed for existing ABCs (TABL + ABCs). In TABL + ABCs, the search direction in the employed bee stage is guided by learning the ranking biased information of the parent food sources, while in the onlooker bee stage, the search direction is determined by extracting the biased information of population distribution. Moreover, a deletion-restart learning strategy is designed in scout bee stage to prevent the potential risk of population stagnation. Systematic experiment results conducted on CEC2014 competition benchmark suite show that proposed TABL + ABCs perform better than recently published AEL + ABCs and ACoS + ABCs.

A Modified PRP-CG Type Derivative-Free Algorithm with Optimal Choices for Solving Large-Scale Nonlinear Symmetric Equations

Inspired by the large number of applications for symmetric nonlinear equations, this article will suggest two optimal choices for the modified Polak–Ribiére–Polyak (PRP) conjugate gradient (CG) method by minimizing the measure function of the search direction matrix and combining the proposed direction with the default Newton direction. In addition, the corresponding PRP parameters are incorporated with the Li and Fukushima approximate gradient to propose two robust CG-type algorithms for finding solutions for large-scale systems of symmetric nonlinear equations. We have also demonstrated the global convergence of the suggested algorithms using some classical assumptions. Finally, we demonstrated the numerical advantages of the proposed algorithms compared to some of the existing methods for nonlinear symmetric equations.

Efficient Resource-Aware Convolutional Neural Architecture Search for Edge Computing with Pareto-Bayesian Optimization

With the development of deep learning technologies and edge computing, the combination of them can make artificial intelligence ubiquitous. Due to the constrained computation resources of the edge device, the research in the field of on-device deep learning not only focuses on the model accuracy but also on the model efficiency, for example, inference latency. There are many attempts to optimize the existing deep learning models for the purpose of deploying them on the edge devices that meet specific application requirements while maintaining high accuracy. Such work not only requires professional knowledge but also needs a lot of experiments, which limits the customization of neural networks for varied devices and application scenarios. In order to reduce the human intervention in designing and optimizing the neural network structure, multi-objective neural architecture search methods that can automatically search for neural networks featured with high accuracy and can satisfy certain hardware performance requirements are proposed. However, the current methods commonly set accuracy and inference latency as the performance indicator during the search process, and sample numerous network structures to obtain the required neural network. Lacking regulation to the search direction with the search objectives will generate a large number of useless networks during the search process, which influences the search efficiency to a great extent. Therefore, in this paper, an efficient resource-aware search method is proposed. Firstly, the network inference consumption profiling model for any specific device is established, and it can help us directly obtain the resource consumption of each operation in the network structure and the inference latency of the entire sampled network. Next, on the basis of the Bayesian search, a resource-aware Pareto Bayesian search is proposed. Accuracy and inference latency are set as the constraints to regulate the search direction. With a clearer search direction, the overall search efficiency will be improved. Furthermore, cell-based structure and lightweight operation are applied to optimize the search space for further enhancing the search efficiency. The experimental results demonstrate that with our method, the inference latency of the searched network structure reduced 94.71% without scarifying the accuracy. At the same time, the search efficiency increased by 18.18%.

A Three-Term Gradient Descent Method with Subspace Techniques

We proposed a three-term gradient descent method that can be well applied to address the optimization problems in this article. The search direction of the obtained method is generated in a specific subspace. Specifically, a quadratic approximation model is applied in the process of generating the search direction. In order to reduce the amount of calculation and make the best use of the existing information, the subspace was made up of the gradient of the current and prior iteration point and the previous search direction. By using the subspace-based optimization technology, the global convergence result is established under Wolfe line search. The results of numerical experiments show that the new method is effective and robust.

Modified Dai-Yuan iterative scheme for Nonlinear Systems and its Application

<p style='text-indent:20px;'>By exploiting the idea employed in the spectral Dai-Yuan method by Xue et al. [IEICE Trans. Inf. Syst. 101 (12)2984-2990 (2018)] and the approach applied in the modified Hager-Zhang scheme for nonsmooth optimization [PLos ONE 11(10): e0164289 (2016)], we develop a Dai-Yuan type iterative scheme for convex constrained nonlinear monotone system. The scheme's algorithm is obtained by combining its search direction with the projection method [Kluwer Academic Publishers, pp. 355-369(1998)]. One of the new scheme's attribute is that it is derivative-free, which makes it ideal for solving non-smooth problems. Furthermore, we demonstrate the method's application in image de-blurring problems by comparing its performance with a recent effective method. By employing mild assumptions, global convergence of the scheme is determined and results of some numerical experiments show the method to be favorable compared to some recent iterative methods.</p>