In this paper,algorithms for finding the inverse of a factor block circulant matrix, a factor block retrocirculant matrix and partitioned matrix with factor block circulant blocks over the complex field are presented ...In this paper,algorithms for finding the inverse of a factor block circulant matrix, a factor block retrocirculant matrix and partitioned matrix with factor block circulant blocks over the complex field are presented respectively.In addition,two algorithms for the inverse of a factor block circulant matrix over the quaternion division algebra are proposed.展开更多
Extensive studies on selecting recombination operators adaptively,namely,adaptive operator selection(AOS),during the search process of an evolutionary algorithm(EA),have shown that AOS is promising for improving EA...Extensive studies on selecting recombination operators adaptively,namely,adaptive operator selection(AOS),during the search process of an evolutionary algorithm(EA),have shown that AOS is promising for improving EA's performance.A variety of heuristic mechanisms for AOS have been proposed in recent decades,which usually contain two main components:the feature extraction and the policy setting.The feature extraction refers to as extracting relevant features from the information collected during the search process.The policy setting means to set a strategy(or policy)on how to select an operator from a pool of operators based on the extracted feature.Both components are designed by hand in existing studies,which may not be efficient for adapting optimization problems.In this paper,a generalized framework is proposed for learning the components of AOS for one of the main streams of EAs,namely,differential evolution(DE).In the framework,the feature extraction is parameterized as a deep neural network(DNN),while a Dirichlet distribution is considered to be the policy.A reinforcement learning method,named policy gradient,is used to train the DNN.As case studies,the proposed framework is applied to two DEs including the classic DE and a recently-proposed DE,which result in two new algorithms named PG-DE and PG-MPEDE,respectively.Experiments on the Congress of Evolutionary Computation(CEC)2018 test suite show that the proposed new algorithms perform significantly better than their counterparts.Finally,we prove theoretically that the considered classic methods are the special cases of the proposed framework.展开更多
Local search methods are convenient alternatives for solving discrete optimization problems(DOPs).These easy-to-implement methods are able to find approximate optimal solutions within a tolerable time limit.It is know...Local search methods are convenient alternatives for solving discrete optimization problems(DOPs).These easy-to-implement methods are able to find approximate optimal solutions within a tolerable time limit.It is known that the quality of the initial solution greatly affects the quality of the approximated solution found by a local search method.In this paper,we propose to take the initial solution as a random variable and learn its preferable probability distribution.The aim is to sample a good initial solution from the learned distribution so that the local search can find a high-quality solution.We develop two different deep network models to deal with DOPs established on set(the knapsack problem)and graph(the maximum clique problem),respectively.The deep neural network learns the representation of an optimization problem instance and transforms the representation to its probability vector.Experimental results show that given the initial solution sampled from the learned probability distribution,a local search method can acquire much better approximate solutions than the randomly-sampled initial solution on the synthesized knapsack instances and the Erd?s-Rényi random graph instances.Furthermore,with sampled initial solutions,a classical genetic algorithm can achieve better solutions than a random initialized population in solving the maximum clique problems on DIMACS instances.Particularly,we emphasize that the developed models can generalize in dimensions and across graphs with various densities,which is an important advantage on generalizing deep-learning-based optimization algorithms.展开更多
Sparse optimization has attracted increasing attention in numerous areas such as compressed sensing, financial optimization and image processing. In this paper, we first consider a special class of cardinality constra...Sparse optimization has attracted increasing attention in numerous areas such as compressed sensing, financial optimization and image processing. In this paper, we first consider a special class of cardinality constrained optimization problems, which involves box constraints and a singly linear constraint. An efficient approach is provided for calculating the projection over the feasibility set after a careful analysis on the projection subproblem. Then we present several types of projected gradient methods for a general class of cardinality constrained optimization problems. Global convergence of the methods is established under suitable assumptions. Finally, we illustrate some applications of the proposed methods for signal recovery and index tracking.Especially for index tracking, we propose a new model subject to an adaptive upper bound on the sparse portfolio weights. The computational results demonstrate that the proposed projected gradient methods are efficient in terms of solution quality.展开更多
A new algorithm for finding the inverse of a nonsingular scaled factor circulant matrix is presented by the Euclid's algorithm. Extension is made to compute the group inverse and the Moore-Penrose inverse of the sing...A new algorithm for finding the inverse of a nonsingular scaled factor circulant matrix is presented by the Euclid's algorithm. Extension is made to compute the group inverse and the Moore-Penrose inverse of the singular scaled factor circulant matrix. Numerical examples are presented to demonstrate the implementation of the proposed algorithm.展开更多
Tight oil/gas medium is a special porous medium,which plays a significant role in oil and gas exploration.This paper is devoted to the derivation of wave equations in such a media,which take a much simpler form compar...Tight oil/gas medium is a special porous medium,which plays a significant role in oil and gas exploration.This paper is devoted to the derivation of wave equations in such a media,which take a much simpler form compared to the general equations in the poroelasticity theory and can be employed for parameter inversion from seismic data.We start with the fluid and solid motion equations at a pore scale,and deduce the complete Biot’s equations by applying the volume averaging technique.The underlying assumptions are carefully clarified.Moreover,time dependence of the permeability in tight oil/gas media is discussed based on available results from rock physical experiments.Leveraging the Kozeny-Carman equation,time dependence of the porosity is theoretically investigated.We derive the wave equations in tight oil/gas media based on the complete Biot’s equations under some reasonable assumptions on the media.The derived wave equations have the similar form as the diffusiveviscous wave equations.A comparison of the two sets of wave equations reveals explicit relations between the coefficients in diffusive-viscous wave equations and the measurable parameters for the tight oil/gas media.The derived equations are validated by numerical results.Based on the derived equations,reflection and transmission properties for a single tight interlayer are investigated.The numerical results demonstrate that the reflection and transmission of the seismic waves are affected by the thickness and attenuation of the interlayer,which is of great significance for the exploration of oil and gas.展开更多
Some mathematical models in geophysics and graphic processing need to compute integrals with scattered data on the sphere.Thus cubature formula plays an important role in computing these spherical integrals.This paper...Some mathematical models in geophysics and graphic processing need to compute integrals with scattered data on the sphere.Thus cubature formula plays an important role in computing these spherical integrals.This paper is devoted to establishing an exact positive cubature formula for spherical basis function networks.The authors give an existence proof of the exact positive cubature formula for spherical basis function networks,and prove that the cubature points needed in the cubature formula are not larger than the number of the scattered data.展开更多
Holub proved that any bounded linear operator T or -T defined on Banach space L 1(μ) satisfies Daugavet equation1+‖T‖=Max{‖I+T‖, ‖I-T‖}.Holub’s theorem is generalized to the nonlinear case: any nonlinear Lipsc...Holub proved that any bounded linear operator T or -T defined on Banach space L 1(μ) satisfies Daugavet equation1+‖T‖=Max{‖I+T‖, ‖I-T‖}.Holub’s theorem is generalized to the nonlinear case: any nonlinear Lipschitz operator f defined on Banach space l 1 satisfies1+L(f)=Max{L(I+f), L(I-f)},where L(f) is the Lipschitz constant of f. The generalized Holub theorem has important applications in characterizing the invertibility of nonlinear operator.展开更多
基金The research is partially supported by the 35th Postdoctoral Work of the National Science Foundation of China(2004035684).
文摘In this paper,algorithms for finding the inverse of a factor block circulant matrix, a factor block retrocirculant matrix and partitioned matrix with factor block circulant blocks over the complex field are presented respectively.In addition,two algorithms for the inverse of a factor block circulant matrix over the quaternion division algebra are proposed.
基金supported by National Natural Science Foundation of China(Grant No.62076197)Key Research and Development Project of Shaanxi Province(Grant No.2022GXLH-01-15)。
文摘Extensive studies on selecting recombination operators adaptively,namely,adaptive operator selection(AOS),during the search process of an evolutionary algorithm(EA),have shown that AOS is promising for improving EA's performance.A variety of heuristic mechanisms for AOS have been proposed in recent decades,which usually contain two main components:the feature extraction and the policy setting.The feature extraction refers to as extracting relevant features from the information collected during the search process.The policy setting means to set a strategy(or policy)on how to select an operator from a pool of operators based on the extracted feature.Both components are designed by hand in existing studies,which may not be efficient for adapting optimization problems.In this paper,a generalized framework is proposed for learning the components of AOS for one of the main streams of EAs,namely,differential evolution(DE).In the framework,the feature extraction is parameterized as a deep neural network(DNN),while a Dirichlet distribution is considered to be the policy.A reinforcement learning method,named policy gradient,is used to train the DNN.As case studies,the proposed framework is applied to two DEs including the classic DE and a recently-proposed DE,which result in two new algorithms named PG-DE and PG-MPEDE,respectively.Experiments on the Congress of Evolutionary Computation(CEC)2018 test suite show that the proposed new algorithms perform significantly better than their counterparts.Finally,we prove theoretically that the considered classic methods are the special cases of the proposed framework.
基金supported by National Natural Science Foundation of China(Grant Nos.11991023 and 62076197)Key Research and Development Project of Shaanxi Province(Grant No.2022GXLH01-15)。
文摘Local search methods are convenient alternatives for solving discrete optimization problems(DOPs).These easy-to-implement methods are able to find approximate optimal solutions within a tolerable time limit.It is known that the quality of the initial solution greatly affects the quality of the approximated solution found by a local search method.In this paper,we propose to take the initial solution as a random variable and learn its preferable probability distribution.The aim is to sample a good initial solution from the learned distribution so that the local search can find a high-quality solution.We develop two different deep network models to deal with DOPs established on set(the knapsack problem)and graph(the maximum clique problem),respectively.The deep neural network learns the representation of an optimization problem instance and transforms the representation to its probability vector.Experimental results show that given the initial solution sampled from the learned probability distribution,a local search method can acquire much better approximate solutions than the randomly-sampled initial solution on the synthesized knapsack instances and the Erd?s-Rényi random graph instances.Furthermore,with sampled initial solutions,a classical genetic algorithm can achieve better solutions than a random initialized population in solving the maximum clique problems on DIMACS instances.Particularly,we emphasize that the developed models can generalize in dimensions and across graphs with various densities,which is an important advantage on generalizing deep-learning-based optimization algorithms.
基金supported by National Natural Science Foundation of China (Grant Nos. 11571271,11631013,11331012 and 71331001)the National Science Fund for Distinguished Young Scholars (Grant No. 11125107)the National 973 Program of China (Grant Nos. 2015CB856002 and 2013CB329404)
文摘Sparse optimization has attracted increasing attention in numerous areas such as compressed sensing, financial optimization and image processing. In this paper, we first consider a special class of cardinality constrained optimization problems, which involves box constraints and a singly linear constraint. An efficient approach is provided for calculating the projection over the feasibility set after a careful analysis on the projection subproblem. Then we present several types of projected gradient methods for a general class of cardinality constrained optimization problems. Global convergence of the methods is established under suitable assumptions. Finally, we illustrate some applications of the proposed methods for signal recovery and index tracking.Especially for index tracking, we propose a new model subject to an adaptive upper bound on the sparse portfolio weights. The computational results demonstrate that the proposed projected gradient methods are efficient in terms of solution quality.
基金supported by the Postdoctoral grants of the Science Foundation of China (Project No.2004035684)
文摘A new algorithm for finding the inverse of a nonsingular scaled factor circulant matrix is presented by the Euclid's algorithm. Extension is made to compute the group inverse and the Moore-Penrose inverse of the singular scaled factor circulant matrix. Numerical examples are presented to demonstrate the implementation of the proposed algorithm.
基金the National Natural Science Foundation of China(Grant Nos.41390450,41390454,91730306)the National Science and Technology Major Projects(Grant Nos.2016ZX05024-001-007,2017ZX05069)the National Key R&D Program of the Ministry of Science and Technology of China(Grant No.2018YFC0603501)。
文摘Tight oil/gas medium is a special porous medium,which plays a significant role in oil and gas exploration.This paper is devoted to the derivation of wave equations in such a media,which take a much simpler form compared to the general equations in the poroelasticity theory and can be employed for parameter inversion from seismic data.We start with the fluid and solid motion equations at a pore scale,and deduce the complete Biot’s equations by applying the volume averaging technique.The underlying assumptions are carefully clarified.Moreover,time dependence of the permeability in tight oil/gas media is discussed based on available results from rock physical experiments.Leveraging the Kozeny-Carman equation,time dependence of the porosity is theoretically investigated.We derive the wave equations in tight oil/gas media based on the complete Biot’s equations under some reasonable assumptions on the media.The derived wave equations have the similar form as the diffusiveviscous wave equations.A comparison of the two sets of wave equations reveals explicit relations between the coefficients in diffusive-viscous wave equations and the measurable parameters for the tight oil/gas media.The derived equations are validated by numerical results.Based on the derived equations,reflection and transmission properties for a single tight interlayer are investigated.The numerical results demonstrate that the reflection and transmission of the seismic waves are affected by the thickness and attenuation of the interlayer,which is of great significance for the exploration of oil and gas.
基金Acknowledgements This work was supported in part by the Science Foundation of the Education Department of Shaanxi Province of China (No. 2013JK0593), the Scientific Research Foundation of Xi'an Polytechnic University (No. BS1014), the China Postdoctoral Science Foundation (No. 20110491668), and the National Natural Science Foundations of China (Grant Nos. 11201362, 11271297, 11101325, 11171270).
文摘光线模式矩阵和光线矩阵的定义第一被建议在一般 H 矩阵的 nonsingularity/singularity 和集中上建立一些新结果。然后矩阵 A 上的一些条件 < 啜 class= “ a-plus-plus ” >
基金Project supported by the Key Program of the National Natural Science Foundation of China(No.11131006)the National Natural Science Foundation of China(Nos.61075054,90818020,60873206)
文摘Some mathematical models in geophysics and graphic processing need to compute integrals with scattered data on the sphere.Thus cubature formula plays an important role in computing these spherical integrals.This paper is devoted to establishing an exact positive cubature formula for spherical basis function networks.The authors give an existence proof of the exact positive cubature formula for spherical basis function networks,and prove that the cubature points needed in the cubature formula are not larger than the number of the scattered data.
文摘Holub proved that any bounded linear operator T or -T defined on Banach space L 1(μ) satisfies Daugavet equation1+‖T‖=Max{‖I+T‖, ‖I-T‖}.Holub’s theorem is generalized to the nonlinear case: any nonlinear Lipschitz operator f defined on Banach space l 1 satisfies1+L(f)=Max{L(I+f), L(I-f)},where L(f) is the Lipschitz constant of f. The generalized Holub theorem has important applications in characterizing the invertibility of nonlinear operator.