Spectrum management and resource allocation(RA)problems are challenging and critical in a vast number of research areas such as wireless communications and computer networks.The traditional approaches for solving such...Spectrum management and resource allocation(RA)problems are challenging and critical in a vast number of research areas such as wireless communications and computer networks.The traditional approaches for solving such problems usually consume time and memory,especially for large-size problems.Recently different machine learning approaches have been considered as potential promising techniques for combinatorial optimization problems,especially the generative model of the deep neural networks.In this work,we propose a resource allocation deep autoencoder network,as one of the promising generative models,for enabling spectrum sharing in underlay device-to-device(D2D)communication by solving linear sum assignment problems(LSAPs).Specifically,we investigate the performance of three different architectures for the conditional variational autoencoders(CVAE).The three proposed architecture are the convolutional neural network(CVAECNN)autoencoder,the feed-forward neural network(CVAE-FNN)autoencoder,and the hybrid(H-CVAE)autoencoder.The simulation results show that the proposed approach could be used as a replacement of the conventional RA techniques,such as the Hungarian algorithm,due to its ability to find solutions of LASPs of different sizes with high accuracy and very fast execution time.Moreover,the simulation results reveal that the accuracy of the proposed hybrid autoencoder architecture outperforms the other proposed architectures and the state-of-the-art DNN techniques.展开更多
Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate...Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate this impulse game problem with the modified objective function including interaction costs among the players in a discontinuous fashion,and subsequently,to derive a verification theorem for identifying the feedback Nash equilibrium strategy.展开更多
The aim of this article is to present new existence results for globally efficient solutions of a strong vector equilibrium problem given by a sum of two functions via a generalized KKM principle, and to establish the...The aim of this article is to present new existence results for globally efficient solutions of a strong vector equilibrium problem given by a sum of two functions via a generalized KKM principle, and to establish the connectedness of the solutions set.展开更多
The sum of reciprocals of Mersenne primes converges to 0.51645417894078856533···, which is an example of a probably infinite subset of primes whose sum of reciprocals is finite and can be computed accur...The sum of reciprocals of Mersenne primes converges to 0.51645417894078856533···, which is an example of a probably infinite subset of primes whose sum of reciprocals is finite and can be computed accurately. This value is larger than , where ?is the set of perfect powers of prime numbers.展开更多
The main purpose of this paper is to extend the Zolotarev's problem concerning with geometric random sums to negative binomial random sums of independent identically distributed random variables.This extension is ...The main purpose of this paper is to extend the Zolotarev's problem concerning with geometric random sums to negative binomial random sums of independent identically distributed random variables.This extension is equivalent to describing all negative binomial infinitely divisible random variables and related results.Using Trotter-operator technique together with Zolotarev-distance's ideality,some upper bounds of convergence rates of normalized negative binomial random sums(in the sense of convergence in distribution)to Gamma,generalized Laplace and generalized Linnik random variables are established.The obtained results are extension and generalization of several known results related to geometric random sums.展开更多
In this paper,we establish some general sums-difference inequalities with two variables.The inequalities involve finite sum and every term contains the unknown function of the composite function with the power of pi.I...In this paper,we establish some general sums-difference inequalities with two variables.The inequalities involve finite sum and every term contains the unknown function of the composite function with the power of pi.In the end,we study boundedness of the solution of the difference equations as applications.展开更多
线性乘积和规划已出现在工程实践和管理科学等领域,是一类NP-难问题。针对该问题目标函数的特殊结构,将其重构为一个D.C.(difference of convex functions)规划问题。再利用凹函数的凸包络,构造出了一种D.C.松弛问题,并将其分解为两个...线性乘积和规划已出现在工程实践和管理科学等领域,是一类NP-难问题。针对该问题目标函数的特殊结构,将其重构为一个D.C.(difference of convex functions)规划问题。再利用凹函数的凸包络,构造出了一种D.C.松弛问题,并将其分解为两个凸子问题。然后将该D.C.松弛与超矩形的标准二分法相结合,设计了新的分支定界算法,并分析了其理论收敛性和计算复杂度。最后,借助大量数值实验验证了该算法的有效性。展开更多
This article presents an image space branch-reduction-bound algorithm for globally solving the sum of affine ratios problem. The algorithm works by solving its equivalent problem, and by using convex hull and concave ...This article presents an image space branch-reduction-bound algorithm for globally solving the sum of affine ratios problem. The algorithm works by solving its equivalent problem, and by using convex hull and concave hull approximation of bilinear function, we can construct the affine relaxation problem of the equivalent problem, which can be used to compute the lower bounds during the branch-and-bound search. By subsequently refining the initial image space rectangle and solving a series of affine relaxation problems, the proposed algorithm is convergent to the global optima of the primal problem. For improving the convergence speed, an image space region reducing method is adopted for compressing the investigated image space rectangle. In addition, the global convergence of the algorithm is proved, and its computational complexity is analyzed. Finally, comparing with some existing methods, numerical results indicate that the algorithm has better computational performance.展开更多
基金supported in part by the China NSFC Grant 61872248Guangdong NSF 2017A030312008+1 种基金Fok Ying-Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (Grant No.161064)GDUPS (2015)
文摘Spectrum management and resource allocation(RA)problems are challenging and critical in a vast number of research areas such as wireless communications and computer networks.The traditional approaches for solving such problems usually consume time and memory,especially for large-size problems.Recently different machine learning approaches have been considered as potential promising techniques for combinatorial optimization problems,especially the generative model of the deep neural networks.In this work,we propose a resource allocation deep autoencoder network,as one of the promising generative models,for enabling spectrum sharing in underlay device-to-device(D2D)communication by solving linear sum assignment problems(LSAPs).Specifically,we investigate the performance of three different architectures for the conditional variational autoencoders(CVAE).The three proposed architecture are the convolutional neural network(CVAECNN)autoencoder,the feed-forward neural network(CVAE-FNN)autoencoder,and the hybrid(H-CVAE)autoencoder.The simulation results show that the proposed approach could be used as a replacement of the conventional RA techniques,such as the Hungarian algorithm,due to its ability to find solutions of LASPs of different sizes with high accuracy and very fast execution time.Moreover,the simulation results reveal that the accuracy of the proposed hybrid autoencoder architecture outperforms the other proposed architectures and the state-of-the-art DNN techniques.
基金supported in part by the National Natural Science Foundation of China(62173051)the Fundamental Research Funds for the Central Universities(2024CDJCGJ012,2023CDJXY-010)+1 种基金the Chongqing Technology Innovation and Application Development Special Key Project(CSTB2022TIADCUX0015,CSTB2022TIAD-KPX0162)the China Postdoctoral Science Foundation(2024M763865)
文摘Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate this impulse game problem with the modified objective function including interaction costs among the players in a discontinuous fashion,and subsequently,to derive a verification theorem for identifying the feedback Nash equilibrium strategy.
文摘The aim of this article is to present new existence results for globally efficient solutions of a strong vector equilibrium problem given by a sum of two functions via a generalized KKM principle, and to establish the connectedness of the solutions set.
文摘The sum of reciprocals of Mersenne primes converges to 0.51645417894078856533···, which is an example of a probably infinite subset of primes whose sum of reciprocals is finite and can be computed accurately. This value is larger than , where ?is the set of perfect powers of prime numbers.
文摘The main purpose of this paper is to extend the Zolotarev's problem concerning with geometric random sums to negative binomial random sums of independent identically distributed random variables.This extension is equivalent to describing all negative binomial infinitely divisible random variables and related results.Using Trotter-operator technique together with Zolotarev-distance's ideality,some upper bounds of convergence rates of normalized negative binomial random sums(in the sense of convergence in distribution)to Gamma,generalized Laplace and generalized Linnik random variables are established.The obtained results are extension and generalization of several known results related to geometric random sums.
基金Supported by the National Natural Science Foundation of China(Grant No.11561019)the Fundamental Research Funds for the Central Universities(Grant No.2012017yjsy141)
文摘In this paper,we establish some general sums-difference inequalities with two variables.The inequalities involve finite sum and every term contains the unknown function of the composite function with the power of pi.In the end,we study boundedness of the solution of the difference equations as applications.
文摘线性乘积和规划已出现在工程实践和管理科学等领域,是一类NP-难问题。针对该问题目标函数的特殊结构,将其重构为一个D.C.(difference of convex functions)规划问题。再利用凹函数的凸包络,构造出了一种D.C.松弛问题,并将其分解为两个凸子问题。然后将该D.C.松弛与超矩形的标准二分法相结合,设计了新的分支定界算法,并分析了其理论收敛性和计算复杂度。最后,借助大量数值实验验证了该算法的有效性。
基金supported by the National Natural Science Foundation of China(Grant Nos.11871196,12071133,12071112)by the Key Scientific and Technological Research Projects of Henan Province(Grant Nos.232102211085,202102210147)+1 种基金by the China Postdoctoral Science Foundation(Grant No.2017M622340)by the Science and Technology Climbing Program of Henan Institute of Science and Technology(Grant No.2018JY01).
文摘This article presents an image space branch-reduction-bound algorithm for globally solving the sum of affine ratios problem. The algorithm works by solving its equivalent problem, and by using convex hull and concave hull approximation of bilinear function, we can construct the affine relaxation problem of the equivalent problem, which can be used to compute the lower bounds during the branch-and-bound search. By subsequently refining the initial image space rectangle and solving a series of affine relaxation problems, the proposed algorithm is convergent to the global optima of the primal problem. For improving the convergence speed, an image space region reducing method is adopted for compressing the investigated image space rectangle. In addition, the global convergence of the algorithm is proved, and its computational complexity is analyzed. Finally, comparing with some existing methods, numerical results indicate that the algorithm has better computational performance.
