In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Comb...In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.展开更多
In this paper,we study a multi-strain SEIR epidemic model with both bilinear and nonmonotone incidence functions.Under biologically motivated assumptions,we show that the model has two basic reproduction numbers that ...In this paper,we study a multi-strain SEIR epidemic model with both bilinear and nonmonotone incidence functions.Under biologically motivated assumptions,we show that the model has two basic reproduction numbers that we noted R0,1 and R0,2;and four equilibrium points.Using the Lyapunov method,we prove that if R0,1 and R0,2 are less than one then the disease-free equilibrium is Globally Asymptotically Stable,thus the disease will be eradicated.However,if one of the two basic reproduction numbers is greater than one,then the strain that persists is that with the larger basic reproduction number.And finally if both of the two basic reproduction numbers are equal or greater than one then the total endemic equilibrium is globally asymptotically stable.A numerical simulation is also presented to illustrate the influence of the psychological effect,of people to infection,on the spread of the disease in the population.This simulation can be used to determine the status of different diseases in a region using the corresponding data and infectious disease parameters.展开更多
In this paper, we propose and analyze a non-monotone trust region method with non-monotone line search strategy for unconstrained optimization problems. Unlike the traditional non-monotone trust region method, our alg...In this paper, we propose and analyze a non-monotone trust region method with non-monotone line search strategy for unconstrained optimization problems. Unlike the traditional non-monotone trust region method, our algorithm utilizes non-monotone Wolfe line search to get the next point if a trial step is not adopted. Thus, it can reduce the number of solving sub-problems. Theoretical analysis shows that the new proposed method has a global convergence under some mild conditions.展开更多
In this paper,a new generalized non-monotonic and saturated incidence rate was introduced into a susceptible-infected-susceptible(SIS)epidemic model to account for inhibitory effect and crowding effect.The dynamic pro...In this paper,a new generalized non-monotonic and saturated incidence rate was introduced into a susceptible-infected-susceptible(SIS)epidemic model to account for inhibitory effect and crowding effect.The dynamic properties of the model were studied by qualitative theory and bifurcation theory.It is shown that when the infuence of psychological factors is large,the model has only disease-free equilibrium point,and this disease-free equilibrium point is globally asymptotically stable;when the influence of psychological factors is small,for some parameter conditions,the model has a unique endemic equilibrium point,which is a cusp point of co-dimension two,and for other parameter conditions the model has two endemic equilibrium points,one of which could be weak focus or center.In addition,the results of the model undergoing saddle-node bifurcation,Hopf bifurcation and Bogdanov-Takens bifurcation as the parameters vary were also proved.These results shed light on the impact of psychological behavior of susceptible people on the disease transmission.展开更多
To investigate the effect of information transmission,Levy jumps and contact heterogeneity of individuals on the asymptotic behavior of epidemic,a stochastic SIQR epidemic model with non-monotone incidence rate and Le...To investigate the effect of information transmission,Levy jumps and contact heterogeneity of individuals on the asymptotic behavior of epidemic,a stochastic SIQR epidemic model with non-monotone incidence rate and Levy jumps on scale-free networks is constructed.At first,the global dynamics of the deterministic model is studied by constructing appropriate Lyapunov functions.Then the stochastic model is made in accordance with the ecological significance,the existence and uniqueness of the global positive solution of the stochastic SIQR model is manifested.Next,by constructing suitable stochastic Lyapunov functions and applying Ito formula with jump,the asymptotic behavior of solutions of stochastic model around equilibrium of the corresponding deterministic model is checked.At last,the correctness of the analytical results is verified by numerical simulations.展开更多
The stability of a periodic oscillation and the global exponential class of recurrent neural networks with non-monotone activation functions and time-varying delays are analyzed. For two sets of activation functions, ...The stability of a periodic oscillation and the global exponential class of recurrent neural networks with non-monotone activation functions and time-varying delays are analyzed. For two sets of activation functions, some algebraic criteria for ascertaining global exponential periodicity and global exponential stability of the class of recurrent neural networks are derived by using the comparison principle and the theory of monotone operator. These conditions are easy to check in terms of system parameters. In addition, we provide a new and efficacious method for the qualitative analysis of various neural networks.展开更多
Abstract In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under ...Abstract In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under the convexity assumption on objective function, the global convergence of the Broyden's class is proved.展开更多
In this paper, we prove the existence in H＋^2, an incomplete metric subspace of H^2×H^2×H^2, of global solutions to the system for a one-dimensional non-monotone fluid in bounded domainΩ=（0,1）. The resul...In this paper, we prove the existence in H＋^2, an incomplete metric subspace of H^2×H^2×H^2, of global solutions to the system for a one-dimensional non-monotone fluid in bounded domainΩ=（0,1）. The results in this paper have improved those previously related results.展开更多
We study the existence of traveling wave solutions for a nonlocal and non-monotone delayed reaction-diffusion equation. Based on the construction of two associated auxiliary reaction diffusion equations with monotonic...We study the existence of traveling wave solutions for a nonlocal and non-monotone delayed reaction-diffusion equation. Based on the construction of two associated auxiliary reaction diffusion equations with monotonicity and by using the traveling wavefronts of the auxiliary equations, the existence of the positive traveling wave solutions for c 〉 c. is obtained. Also, the exponential asymptotic behavior in the negative infinity was established. Moreover, we apply our results to some reactiondiffusion equations with spatio-temporal delay to obtain the existence of traveling waves. These results cover, complement and/or improve some existing ones in the literature.展开更多
We consider a one-dimensional continuous thermal model of nuclear matter, which is described by a compressible Navier-Stokes-Poission system with a non-monotone equation of state owing to the effective Skyrme nuclear ...We consider a one-dimensional continuous thermal model of nuclear matter, which is described by a compressible Navier-Stokes-Poission system with a non-monotone equation of state owing to the effective Skyrme nuclear interaction between particles. We prove the global existence of solutions in H^4 space for a free boundary value problem with a possible destabilizing influence of the pressure which is not always positive,provided a sufficient thermal dissipation is present and first obtain the existence of classical solutions.展开更多
The advantage of multi-protocol label switching (MPLS) is its capability to route the packets through explicit paths. But the nodes in the paths may be possibly attacked by the adversarial uncertainty. Aiming at this ...The advantage of multi-protocol label switching (MPLS) is its capability to route the packets through explicit paths. But the nodes in the paths may be possibly attacked by the adversarial uncertainty. Aiming at this problem in MPLS Network, in this paper, we propose a novel mechanism in MPLS network under adversar-ial uncertainty, making use of the theory of artificial intelligence, at first, we find the initialized label switching paths (LSPs) using the A* arithmetic, and secondly, during the process of data transmission, we switch the transmission path duly by taking advantage of the non-monotone reasoning mechanism. Com-pared to the traditional route mechanism, the experimental results show that it improves the security if data transmission remarkably under our novel mechanism in MPLS network.展开更多
We consider a one-dimensional continuous model of nutron star, described by a compressible thermoviscoelastic system with a non-monotone equation of state, due to the effective Skyrme nuclear interaction between parti...We consider a one-dimensional continuous model of nutron star, described by a compressible thermoviscoelastic system with a non-monotone equation of state, due to the effective Skyrme nuclear interaction between particles. We will prove that, despite a possible destabilizing influence of the pressure, which is non-monotone and not always positive, the presence of viscosity and a sufficient thermal dissipation describe the global existence of solutions in H^4 with a mixed free boundary problem for our model.展开更多
The pooling problem,also called the blending problem,is fundamental in production planning of petroleum.It can be formulated as an optimization problem similar with the minimum-cost flow problem.However,Alfaki and Hau...The pooling problem,also called the blending problem,is fundamental in production planning of petroleum.It can be formulated as an optimization problem similar with the minimum-cost flow problem.However,Alfaki and Haugland(J Glob Optim 56:897–916,2013)proved the strong NP-hardness of the pooling problem in general case.They also pointed out that it was an open problem to determine the computational complexity of the pooling problem with a fixed number of qualities.In this paper,we prove that the pooling problem is still strongly NP-hard even with only one quality.This means the quality is an essential difference between minimum-cost flow problem and the pooling problem.For solving large-scale pooling problems in real applications,we adopt the non-monotone strategy to improve the traditional successive linear programming method.Global convergence of the algorithm is established.The numerical experiments show that the non-monotone strategy is effective to push the algorithm to explore the global minimizer or provide a good local minimizer.Our results for real problems from factories show that the proposed algorithm is competitive to the one embedded in the famous commercial software Aspen PIMS.展开更多
This paper is concerned with the stability of non-monotone traveling waves for a discrete diffusion equation with monostable convolution type nonlinearity. By using the anti-weighted energy method and nonlinear Halana...This paper is concerned with the stability of non-monotone traveling waves for a discrete diffusion equation with monostable convolution type nonlinearity. By using the anti-weighted energy method and nonlinear Halanay's inequality, we prove that all noncritical traveling waves(waves with speeds c > c_*, c_* is minimal speed) are time-exponentially stable, when the initial perturbations around the waves are small. As a corollary of our stability result, we immediately obtain the uniqueness of the traveling waves.展开更多
The initial value problem of the multi-dimensional drift-flux model for two-phase flow is investigated in this paper,and the global existence of weak solutions with finite energy is established for general pressure-de...The initial value problem of the multi-dimensional drift-flux model for two-phase flow is investigated in this paper,and the global existence of weak solutions with finite energy is established for general pressure-density functions without the monotonicity assumption.展开更多
The integration of different heterogeneous access networks is one of the remarkable characteristics of the next generation network,in which users with multi-network interface terminals can independently select access ...The integration of different heterogeneous access networks is one of the remarkable characteristics of the next generation network,in which users with multi-network interface terminals can independently select access network to obtain the most desired service.A kind of unified quantification model of non-monotone quality of service(QoS) and a model of non-cooperative game between users and networks are proposed for heterogeneous network access selection.An optimal network pricing mechanism could be formulated by using a novel strategy which is used in this non-cooperative game model to balance the interests of both the users and the networks.This access network selection mechanism could select the most suitable network for users,and it also could provide the basis when formulating QoS standards in heterogeneous integrated networks.The simulation results show that this network selection decision-making algorithm can meet the users' demand for different levels service in different scenes and it can also avoid network congestion caused by unbalanced load.展开更多
文摘In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.
文摘In this paper,we study a multi-strain SEIR epidemic model with both bilinear and nonmonotone incidence functions.Under biologically motivated assumptions,we show that the model has two basic reproduction numbers that we noted R0,1 and R0,2;and four equilibrium points.Using the Lyapunov method,we prove that if R0,1 and R0,2 are less than one then the disease-free equilibrium is Globally Asymptotically Stable,thus the disease will be eradicated.However,if one of the two basic reproduction numbers is greater than one,then the strain that persists is that with the larger basic reproduction number.And finally if both of the two basic reproduction numbers are equal or greater than one then the total endemic equilibrium is globally asymptotically stable.A numerical simulation is also presented to illustrate the influence of the psychological effect,of people to infection,on the spread of the disease in the population.This simulation can be used to determine the status of different diseases in a region using the corresponding data and infectious disease parameters.
文摘In this paper, we propose and analyze a non-monotone trust region method with non-monotone line search strategy for unconstrained optimization problems. Unlike the traditional non-monotone trust region method, our algorithm utilizes non-monotone Wolfe line search to get the next point if a trial step is not adopted. Thus, it can reduce the number of solving sub-problems. Theoretical analysis shows that the new proposed method has a global convergence under some mild conditions.
基金supported by the NSF of China[Grant No.11961021]the NSF of Guangdong province[Grant Nos.2022A1515010964 and 2022A1515010193]+1 种基金the Innovation and Developing School Project of Guangdong Province[Grant No.2019KzDXM032]the Special Fund of Science and Technology Innovation Strategy of Guangdong Province[Grant Nos.pdjh2022b0320 and pdjh2023b0325].
文摘In this paper,a new generalized non-monotonic and saturated incidence rate was introduced into a susceptible-infected-susceptible(SIS)epidemic model to account for inhibitory effect and crowding effect.The dynamic properties of the model were studied by qualitative theory and bifurcation theory.It is shown that when the infuence of psychological factors is large,the model has only disease-free equilibrium point,and this disease-free equilibrium point is globally asymptotically stable;when the influence of psychological factors is small,for some parameter conditions,the model has a unique endemic equilibrium point,which is a cusp point of co-dimension two,and for other parameter conditions the model has two endemic equilibrium points,one of which could be weak focus or center.In addition,the results of the model undergoing saddle-node bifurcation,Hopf bifurcation and Bogdanov-Takens bifurcation as the parameters vary were also proved.These results shed light on the impact of psychological behavior of susceptible people on the disease transmission.
基金supported by the Natural Science Foundation of Ningxia(Grant 2021AAC03030).
文摘To investigate the effect of information transmission,Levy jumps and contact heterogeneity of individuals on the asymptotic behavior of epidemic,a stochastic SIQR epidemic model with non-monotone incidence rate and Levy jumps on scale-free networks is constructed.At first,the global dynamics of the deterministic model is studied by constructing appropriate Lyapunov functions.Then the stochastic model is made in accordance with the ecological significance,the existence and uniqueness of the global positive solution of the stochastic SIQR model is manifested.Next,by constructing suitable stochastic Lyapunov functions and applying Ito formula with jump,the asymptotic behavior of solutions of stochastic model around equilibrium of the corresponding deterministic model is checked.At last,the correctness of the analytical results is verified by numerical simulations.
基金Supported by the Natural Science Foundation of Hubei Province (2007ABA124)the Youth Project Foundation of Hubei Province Education Department (Q200722001)the Major Foundation of Hubei Province Education Department (D200722002)
文摘The stability of a periodic oscillation and the global exponential class of recurrent neural networks with non-monotone activation functions and time-varying delays are analyzed. For two sets of activation functions, some algebraic criteria for ascertaining global exponential periodicity and global exponential stability of the class of recurrent neural networks are derived by using the comparison principle and the theory of monotone operator. These conditions are easy to check in terms of system parameters. In addition, we provide a new and efficacious method for the qualitative analysis of various neural networks.
基金Partly supported by the National Natural Sciences Foundation of China (No. 19731001)National 973 Information Technology and High-Performance Software Program of China (No.G1998030401)K.C.Wong Education Foundation, Hong Kong.
文摘Abstract In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under the convexity assumption on objective function, the global convergence of the Broyden's class is proved.
文摘In this paper, we prove the existence in H＋^2, an incomplete metric subspace of H^2×H^2×H^2, of global solutions to the system for a one-dimensional non-monotone fluid in bounded domainΩ=（0,1）. The results in this paper have improved those previously related results.
基金Supported by National Natural Science Foundation of China(Grant No.11171120)the Doctoral Program of Higher Education of China(Grant No.20094407110001)the Natural Science Foundation of Guangdong Province(Grant Nos.1015106310100003 and S2012010010034)
文摘We study the existence of traveling wave solutions for a nonlocal and non-monotone delayed reaction-diffusion equation. Based on the construction of two associated auxiliary reaction diffusion equations with monotonicity and by using the traveling wavefronts of the auxiliary equations, the existence of the positive traveling wave solutions for c 〉 c. is obtained. Also, the exponential asymptotic behavior in the negative infinity was established. Moreover, we apply our results to some reactiondiffusion equations with spatio-temporal delay to obtain the existence of traveling waves. These results cover, complement and/or improve some existing ones in the literature.
基金Supported by the National Natural Science Foundation of China(No.11701465)
文摘We consider a one-dimensional continuous thermal model of nuclear matter, which is described by a compressible Navier-Stokes-Poission system with a non-monotone equation of state owing to the effective Skyrme nuclear interaction between particles. We prove the global existence of solutions in H^4 space for a free boundary value problem with a possible destabilizing influence of the pressure which is not always positive,provided a sufficient thermal dissipation is present and first obtain the existence of classical solutions.
文摘The advantage of multi-protocol label switching (MPLS) is its capability to route the packets through explicit paths. But the nodes in the paths may be possibly attacked by the adversarial uncertainty. Aiming at this problem in MPLS Network, in this paper, we propose a novel mechanism in MPLS network under adversar-ial uncertainty, making use of the theory of artificial intelligence, at first, we find the initialized label switching paths (LSPs) using the A* arithmetic, and secondly, during the process of data transmission, we switch the transmission path duly by taking advantage of the non-monotone reasoning mechanism. Com-pared to the traditional route mechanism, the experimental results show that it improves the security if data transmission remarkably under our novel mechanism in MPLS network.
文摘We consider a one-dimensional continuous model of nutron star, described by a compressible thermoviscoelastic system with a non-monotone equation of state, due to the effective Skyrme nuclear interaction between particles. We will prove that, despite a possible destabilizing influence of the pressure, which is non-monotone and not always positive, the presence of viscosity and a sufficient thermal dissipation describe the global existence of solutions in H^4 with a mixed free boundary problem for our model.
基金This research is supported by the National Natural Science Foundation of China(Nos.11631013,71331001,11331012)the National 973 Program of China(No.2015CB856002).
文摘The pooling problem,also called the blending problem,is fundamental in production planning of petroleum.It can be formulated as an optimization problem similar with the minimum-cost flow problem.However,Alfaki and Haugland(J Glob Optim 56:897–916,2013)proved the strong NP-hardness of the pooling problem in general case.They also pointed out that it was an open problem to determine the computational complexity of the pooling problem with a fixed number of qualities.In this paper,we prove that the pooling problem is still strongly NP-hard even with only one quality.This means the quality is an essential difference between minimum-cost flow problem and the pooling problem.For solving large-scale pooling problems in real applications,we adopt the non-monotone strategy to improve the traditional successive linear programming method.Global convergence of the algorithm is established.The numerical experiments show that the non-monotone strategy is effective to push the algorithm to explore the global minimizer or provide a good local minimizer.Our results for real problems from factories show that the proposed algorithm is competitive to the one embedded in the famous commercial software Aspen PIMS.
基金supported by National Natural Science Foundation of China(Grant No.11401478)
文摘This paper is concerned with the stability of non-monotone traveling waves for a discrete diffusion equation with monostable convolution type nonlinearity. By using the anti-weighted energy method and nonlinear Halanay's inequality, we prove that all noncritical traveling waves(waves with speeds c > c_*, c_* is minimal speed) are time-exponentially stable, when the initial perturbations around the waves are small. As a corollary of our stability result, we immediately obtain the uniqueness of the traveling waves.
基金supported by National Natural Science Foundation of China(Grant Nos.11931010,11671384 and 11871047)the key research project of Academy for Multidisciplinary Studies,Capital Normal Universitythe Capacity Building for Sci-Tech Innovation-Fundamental Scientific Research Funds(Grant No.007/20530290068)。
文摘The initial value problem of the multi-dimensional drift-flux model for two-phase flow is investigated in this paper,and the global existence of weak solutions with finite energy is established for general pressure-density functions without the monotonicity assumption.
基金Supported by the National Natural Science Foundation of China(No.61272120)the Science and Technology Project of Xi'an(No.CXY1117(5))
文摘The integration of different heterogeneous access networks is one of the remarkable characteristics of the next generation network,in which users with multi-network interface terminals can independently select access network to obtain the most desired service.A kind of unified quantification model of non-monotone quality of service(QoS) and a model of non-cooperative game between users and networks are proposed for heterogeneous network access selection.An optimal network pricing mechanism could be formulated by using a novel strategy which is used in this non-cooperative game model to balance the interests of both the users and the networks.This access network selection mechanism could select the most suitable network for users,and it also could provide the basis when formulating QoS standards in heterogeneous integrated networks.The simulation results show that this network selection decision-making algorithm can meet the users' demand for different levels service in different scenes and it can also avoid network congestion caused by unbalanced load.
