In this article, we investigate monotone and Lipschitz continuous variational inclusion problem in the settings of Hadamard manifolds. We propose a forward–backward method with a self-adaptive technique for solving variational inclusion problem. To increase the rate of convergence of our proposed method, we incorporate our iterative method with double inertial steps and establish...
In modeling the bilateral selection of states of the process, Dynkin (Dokl Akad Nauk USSR 185:241–288, 1969) proposed a two-person game in which players use stopping moments as strategies. The purpose of this work is to present a model of the game in which the players have different information about the process itself, as well as various laws to stop the process and accept its...
The development of convergent technology makes the drone expected to become a commercial delivery method for terminal logistics distribution. Although the industry has begun to experiment with the coordinated transportation of drones and vehicles, some limited assumptions have been made to reduce the complexity of synchronization. This paper studies the mathematical formulations...
There exist linear relations among tensor entries of low rank tensors. These linear relations can be expressed by multi-linear polynomials, which are called generating polynomials. We use generating polynomials to compute tensor rank decompositions and low rank tensor approximations. We prove that this gives a quasi-optimal low rank tensor approximation if the given tensor is...
Numerous intriguing optimization problems arise as a result of the advancement of machine learning. The stochastic first-order method is the predominant choice for those problems due to its high efficiency. However, the negative effects of noisy gradient estimates and high nonlinearity of the loss function result in a slow convergence rate. Second-order algorithms have their...
This work considers a long-term Perishable Inventory Routing Problem with multiple products, static demand, and single vehicle, in the setting of Vendor Managed Inventory. By analyzing the optimal solutions of long-term cases that can be solved in Python+Gurobi within 2 h, we capture some patterns of optimal solutions. Utilizing these patterns, experiments show that under certain...
The pandemic of COVID-19 initiated in 2019 and spread all over the world in 2020 has caused significant damages to the human society, making troubles to all aspects of our daily life. Facing the serious outbreak of the virus, we consider possible solutions from the perspectives of both governments and enterprises. Particularly, this paper discusses several applications of supply...
The distribution–allocation problem is known as one of the most comprehensive strategic decisions. In real-world cases, it is impossible to solve a distribution–allocation problem completely in acceptable time. This forces the researchers to develop efficient heuristic techniques for the large-term operation of the whole supply chain. These techniques provide near optimal...
Sparse signals can be possibly reconstructed by an algorithm which merges a traditional nonlinear optimization method and a certain thresholding technique. Different from existing thresholding methods, a novel thresholding technique referred to as the optimal k-thresholding was recently proposed by Zhao (SIAM J Optim 30(1):31–55, 2020). This technique simultaneously performs the...
Recently, alternating direction method of multipliers (ADMM) attracts much attentions from various fields and there are many variant versions tailored for different models. Moreover, its theoretical studies such as rate of convergence and extensions to nonconvex problems also achieve much progress. In this paper, we give a survey on some recent developments of ADMM and its variants.
In general, data contain noises which come from faulty instruments, flawed measurements or faulty communication. Learning with data in the context of classification or regression is inevitably affected by noises in the data. In order to remove or greatly reduce the impact of noises, we introduce the ideas of fuzzy membership functions and the Laplacian twin support vector machine...
The authors would like to correct the style of their names in the original publication. The correct style of author names is provided in this correction.
This study develops a holistic view of the novel coronavirus (COVID-19) spread worldwide through a spatial–temporal model with network dynamics. By using a unique human mobility dataset containing 547 166 flights with a total capacity of 101 455 913 passengers from January 22 to April 24, 2020, we analyze the epidemic correlations across 22 countries in six continents and...