No abstract

In this paper, we propose enhancements to Beetle Antennae Search (BAS) algorithm, called BAS-ADAM, to smoothen the convergence behavior and avoid trapping in local-minima for a highly non-convex objective function. We achieve this by adaptively adjusting the step-size in each iteration using the Adaptive Moment Estimation (ADAM) update rule. The proposed algorithm also increases the convergence rate in a narrow valley. A key feature of the ADAM update rule is the ability to adjust the step-size for each dimension separately instead of using the same step-size. Since ADAM is traditionally used with gradient-based optimization algorithms, therefore we first propose a gradient estimation model without the need to differentiate the objective function. Resultantly, it demonstrates excellent performance and fast convergence rate in searching for the optimum of non-convex functions. The efficiency of the proposed algorithm was tested on three different benchmark problems, including the training of a high-dimensional neural network. The performance is compared with Particle Swarm Optimizer (PSO) and the original BAS algorithm.

Abstract. In this article a fast computational method is provided in order to calculate the Moore-Penrose inverse of full rank m × n matrices and of square matrices with at least one zero row or column. Sufficient conditions are also given for special type products of square matrices so that the reverse order law for the Moore-Penrose inverse is satisfied.

This paper presents a fast computational method that finds application in a broad scientific field such as digital image restoration. The proposed method provides a new approach to the problem of image reconstruction by using the Moore-Penrose inverse. The resolution of the reconstructed image remains at a very high level but the main advantage of the method was found on the computational load that has been decreased considerably compared to the classic techniques.