An investigation is carried out on the problem involved in 4D variational data assimilation (VDA) with constraint conditions based on a finite-element shallow-water equation model. In the investigation, the adjoint te...An investigation is carried out on the problem involved in 4D variational data assimilation (VDA) with constraint conditions based on a finite-element shallow-water equation model. In the investigation, the adjoint technology, penalty method and augmented Lagrangian method are used in constraint optimization field to minimize the defined constraint objective functions. The results of the numerical experiments show that the optimal solutions are obtained if the functions reach the minima. VDA with constraint conditions controlling the growth of gravity oscillations is efficient to eliminate perturbation and produces optimal initial field. It seems that this method can also be applied to the problem in numerical weather prediction. Key words Variational data assimilation - Constraint conditions - Penalty methods - finite-element model This research is supported by National Natural Science Foundation of China (Grant No. 49575269) and by National Key Basic Research on the Formation Mechanism and Prediction Theory of Severe Synoptic Disasters (Grant No. G1998040910).展开更多
In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order ...In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.展开更多
In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These co...In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.展开更多
A class of quasilinear elliptic variational inequalities with double degenerate is discussed in this paper. We extend the Keldys-Fichera boundary value problem and the first boundary problem of degenerate elliptic equ...A class of quasilinear elliptic variational inequalities with double degenerate is discussed in this paper. We extend the Keldys-Fichera boundary value problem and the first boundary problem of degenerate elliptic equation to the variationalinequalities. We establish the existence and uniqueness of the weak solution of ocrresspending problem under nonstandard growth conditions.展开更多
The Proton Exchange Membrane Fuel Cell(PEMFC)converts the chemical energy of hydrogen fuel directly into electrical energy with broad application prospects.Understanding how current density is distributed in the PEMFC...The Proton Exchange Membrane Fuel Cell(PEMFC)converts the chemical energy of hydrogen fuel directly into electrical energy with broad application prospects.Understanding how current density is distributed in the PEMFC systems is crucial as it is a key factor influencing system performance.However,direct modeling for current distribution may encounter the challenge of dimensional catastrophe owing to the high dimensionality of the data.This paper uses a high-resolution segmented measurement device with 396 points to conduct experimental tests on the current distribution of a PEMFC with reactive area of 406 cm^(2) during a stepwise increase in load current.The current distribution is modeled based on the test results to learn the mapping relationship between the experimental parameters and the current distribution.The proposed model utilizes a Conditional Variational Auto-Encoder(CVAE)to generate current distributions.The MSE(Mean-Square Error)of the trained CVAE model reaches 9.2×10^(-5),and the comparison results show that the 222.9A current distribution error has the largest MSE of 6.36×10^(-4) and a KL Divergence(Kullback-Leibler Divergence)of 9.55×10^(-4),both of which are at a low level.This model enables the direct determination of the current distribution based on the experimental parameters,thereby establishing a technical foundation for investigating the impact of experimental conditions on fuel cells.This model is also of great significance for research on fuel cell system control strategies and fault diagnosis.展开更多
Future 6G communications will open up opportunities for innovative applications,including Cyber-Physical Systems,edge computing,supporting Industry 5.0,and digital agriculture.While automation is creating efficiencies...Future 6G communications will open up opportunities for innovative applications,including Cyber-Physical Systems,edge computing,supporting Industry 5.0,and digital agriculture.While automation is creating efficiencies,it can also create new cyber threats,such as vulnerabilities in trust and malicious node injection.Denialof-Service(DoS)attacks can stop many forms of operations by overwhelming networks and systems with data noise.Current anomaly detection methods require extensive software changes and only detect static threats.Data collection is important for being accurate,but it is often a slow,tedious,and sometimes inefficient process.This paper proposes a new wavelet transformassisted Bayesian deep learning based probabilistic(WT-BDLP)approach tomitigate malicious data injection attacks in 6G edge networks.The proposed approach combines outlier detection based on a Bayesian learning conditional variational autoencoder(Bay-LCVariAE)and traffic pattern analysis based on continuous wavelet transform(CWT).The Bay-LCVariAE framework allows for probabilistic modelling of generative features to facilitate capturing how features of interest change over time,spatially,and for recognition of anomalies.Similarly,CWT allows emphasizing the multi-resolution spectral analysis and permits temporally relevant frequency pattern recognition.Experimental testing showed that the flexibility of the Bayesian probabilistic framework offers a vast improvement in anomaly detection accuracy over existing methods,with a maximum accuracy of 98.21%recognizing anomalies.展开更多
Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different ...Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether's symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.展开更多
Inverse design has long been an efficient and powerful design tool in the aircraft industry.In this paper,a novel inverse design method for supercritical airfoils is proposed based on generative models in deep learnin...Inverse design has long been an efficient and powerful design tool in the aircraft industry.In this paper,a novel inverse design method for supercritical airfoils is proposed based on generative models in deep learning.A Conditional Variational Auto Encoder(CVAE)and an integrated generative network CVAE-GAN that combines the CVAE with the Wasserstein Generative Adversarial Networks(WGAN),are conducted as generative models.They are used to generate target wall Mach distributions for the inverse design that matches specified features,such as locations of suction peak,shock and aft loading.Qualitative and quantitative results show that both adopted generative models can generate diverse and realistic wall Mach number distributions satisfying the given features.The CVAE-GAN model outperforms the CVAE model and achieves better reconstruction accuracies for all the samples in the dataset.Furthermore,a deep neural network for nonlinear mapping is adopted to obtain the airfoil shape corresponding to the target wall Mach number distribution.The performances of the designed deep neural network are fully demonstrated and a smoothness measurement is proposed to quantify small oscillations in the airfoil surface,proving the authenticity and accuracy of the generated airfoil shapes.展开更多
In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its c...In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its convergence results are established.展开更多
In this paper, a new variational formulation for a reaction-diffusion problem in broken Sobolev space is proposed. And the new formulation in the broken Sobolev space will be proved that it is well-posed and equivalen...In this paper, a new variational formulation for a reaction-diffusion problem in broken Sobolev space is proposed. And the new formulation in the broken Sobolev space will be proved that it is well-posed and equivalent to the standard Galerkin variational formulation. The method will be helpful to easily solve the original partial differential equation numerically. And the method is novel and interesting, which can be used to deal with some complicated problem, such as the low regularity problem, the differential-integral problem and so on.展开更多
One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, ...One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, a new approach method is proposed and the existence of the solution was proved for the BSDEs if the diffusion coefficients satisfy the locally Lipschitz condition. In the special case the solution was a Brownian bridge. The uniqueness is also considered in the meaning of "F0-integrable equivalent class" . The new approach method would give us an efficient way to control the main object instead of the "noise".展开更多
In this paper,through the use of image space analysis,optimality conditions for a class of variational inequalities with cone constraints are proposed.By virtue of the nonlinear scalarization function,known as the Ger...In this paper,through the use of image space analysis,optimality conditions for a class of variational inequalities with cone constraints are proposed.By virtue of the nonlinear scalarization function,known as the Gerstewitz function,three nonlinear weak separation functions,two nonlinear regular weak separation functions and a nonlinear strong separation function are introduced.According to nonlinearseparation functions,some optimality conditions of the weak and strong alternative for variational inequalities with cone constraints are derived.展开更多
To reveal the multivariate relationships between man-made and meteorological factors on dust storm frequency, the LUCC data, NDVI remote sensing data and meteorological data for the period of 1983-2013 were combined w...To reveal the multivariate relationships between man-made and meteorological factors on dust storm frequency, the LUCC data, NDVI remote sensing data and meteorological data for the period of 1983-2013 were combined with dust storm frequency data, and the possible impacts of meteorological and anthropogenic factors on dust storm frequency were analyzed by using regression analysis and PCA (Principal Component Analysis). Results show that the inter-annual dust storm frequency increased gradually. In particular, an increasing trend in recent years, after 2009, is conspicuous. The monthly frequency of dust storms shows higher values between the months of February and May, with the highest mean number of events occurring in April, which accounts for 29% of the annual dust storm frequency. The annual dust storm frequency is positively correlated with wind speed and negatively correlated with precipitation;the monthly dust storm frequency is positively correlated with wind speed, but no significant correlation can be found with precipitation. The relationship between temperature and dust storms is not simply linear, however, a certain correlation with an unremarkable statistical significance can be found between them. Human activities also affect the dynamics of dust storms indirectly via changing vegetation coverage and direct dust emissions. The multivariate analysis further confirmed the association between dust storm frequency and meteorological factors and NDVI. The high loadings of dust storm frequency, wind speed, precipitation and NDVI on a PC indicate that the increased precipitation and NDVI will decrease dust storm frequency, and increased wind speed will increase dust storm frequency.展开更多
The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or schedu...The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or scheduling,and integer partitions.An accurate search algorithm with polynomial time complexity has not been found,which makes it challenging to be solved on classical computers.To effectively solve this problem,we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk.The proposed model needs only n qubits to encode 2ndimensional search space,which can effectively save the encoding quantum resources.The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise,and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era.We investigate the effects of the scalability,the variational ansatz type,the variational depth,and noise on the model.Moreover,we also discuss the performance of the model under different conditional values at risk.Through computer simulation,the scale can reach more than nine qubits.By selecting the noise type,we construct simulators with different QVs and study the performance of the model with them.In addition,we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem.This model provides a new perspective for solving the subset sum problem.展开更多
A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable...A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.展开更多
The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions proble...The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions problem is proposed, and some desirable properties of the merit function are obtained. Through the merit function, the original problem is reformulated as minimization with simple constraints. Then, the authors show that any stationary point of the optimization problem is a solution of the original problem. Finally, a descent algorithm is presented for the optimization problem, and global convergence is shown.展开更多
The variational analysis of the Pseudo-potential function-vortex-potential function model, a new mathematical model, was developed and by which the flow field with transonic speed and curl was decided, and different s...The variational analysis of the Pseudo-potential function-vortex-potential function model, a new mathematical model, was developed and by which the flow field with transonic speed and curl was decided, and different sorts of the variational principle for vortex potential function were established by transforming the original equation for vortex-function, the boundary conditions for vortex-potential function was raised.展开更多
In this article we study the existence of solutions for the Dirac systems with the chirality boundary condition.Using an analytic framework of proper products of fractional Sobolev spaces,the solutions existence resul...In this article we study the existence of solutions for the Dirac systems with the chirality boundary condition.Using an analytic framework of proper products of fractional Sobolev spaces,the solutions existence results of the coupled Dirac systems are obtained for nonlinearity with superquadratic growth rates.The results obtained by GONG and LU(2017)are extended to the case of chiral boundary condition.展开更多
基金National Natural Science Foundation of China (Grant No. 49575269) National Key Basic Research on the Formation Mechanism and
文摘An investigation is carried out on the problem involved in 4D variational data assimilation (VDA) with constraint conditions based on a finite-element shallow-water equation model. In the investigation, the adjoint technology, penalty method and augmented Lagrangian method are used in constraint optimization field to minimize the defined constraint objective functions. The results of the numerical experiments show that the optimal solutions are obtained if the functions reach the minima. VDA with constraint conditions controlling the growth of gravity oscillations is efficient to eliminate perturbation and produces optimal initial field. It seems that this method can also be applied to the problem in numerical weather prediction. Key words Variational data assimilation - Constraint conditions - Penalty methods - finite-element model This research is supported by National Natural Science Foundation of China (Grant No. 49575269) and by National Key Basic Research on the Formation Mechanism and Prediction Theory of Severe Synoptic Disasters (Grant No. G1998040910).
文摘In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.
文摘In this paper, necessary optimality conditions for a class of Semi-infinite Variational Problems are established which are further generalized to a class of Multi-objective Semi-Infinite Variational Problems. These conditions are responsible for the development of duality theory which is an extremely important feature for any class of problems, but the literature available so far lacks these necessary optimality conditions for the stated problem. A lemma is also proved to find the topological dual of as it is required to prove the desired result.
文摘A class of quasilinear elliptic variational inequalities with double degenerate is discussed in this paper. We extend the Keldys-Fichera boundary value problem and the first boundary problem of degenerate elliptic equation to the variationalinequalities. We establish the existence and uniqueness of the weak solution of ocrresspending problem under nonstandard growth conditions.
基金sponsored by Science and Technology Program of Sichuan Province(2024ZDZX0035 and 2024ZHCG0072)。
文摘The Proton Exchange Membrane Fuel Cell(PEMFC)converts the chemical energy of hydrogen fuel directly into electrical energy with broad application prospects.Understanding how current density is distributed in the PEMFC systems is crucial as it is a key factor influencing system performance.However,direct modeling for current distribution may encounter the challenge of dimensional catastrophe owing to the high dimensionality of the data.This paper uses a high-resolution segmented measurement device with 396 points to conduct experimental tests on the current distribution of a PEMFC with reactive area of 406 cm^(2) during a stepwise increase in load current.The current distribution is modeled based on the test results to learn the mapping relationship between the experimental parameters and the current distribution.The proposed model utilizes a Conditional Variational Auto-Encoder(CVAE)to generate current distributions.The MSE(Mean-Square Error)of the trained CVAE model reaches 9.2×10^(-5),and the comparison results show that the 222.9A current distribution error has the largest MSE of 6.36×10^(-4) and a KL Divergence(Kullback-Leibler Divergence)of 9.55×10^(-4),both of which are at a low level.This model enables the direct determination of the current distribution based on the experimental parameters,thereby establishing a technical foundation for investigating the impact of experimental conditions on fuel cells.This model is also of great significance for research on fuel cell system control strategies and fault diagnosis.
文摘Future 6G communications will open up opportunities for innovative applications,including Cyber-Physical Systems,edge computing,supporting Industry 5.0,and digital agriculture.While automation is creating efficiencies,it can also create new cyber threats,such as vulnerabilities in trust and malicious node injection.Denialof-Service(DoS)attacks can stop many forms of operations by overwhelming networks and systems with data noise.Current anomaly detection methods require extensive software changes and only detect static threats.Data collection is important for being accurate,but it is often a slow,tedious,and sometimes inefficient process.This paper proposes a new wavelet transformassisted Bayesian deep learning based probabilistic(WT-BDLP)approach tomitigate malicious data injection attacks in 6G edge networks.The proposed approach combines outlier detection based on a Bayesian learning conditional variational autoencoder(Bay-LCVariAE)and traffic pattern analysis based on continuous wavelet transform(CWT).The Bay-LCVariAE framework allows for probabilistic modelling of generative features to facilitate capturing how features of interest change over time,spatially,and for recognition of anomalies.Similarly,CWT allows emphasizing the multi-resolution spectral analysis and permits temporally relevant frequency pattern recognition.Experimental testing showed that the flexibility of the Bayesian probabilistic framework offers a vast improvement in anomaly detection accuracy over existing methods,with a maximum accuracy of 98.21%recognizing anomalies.
基金supported by CNPq and CAPES(Brazilian research funding agencies)Portuguese funds through the Center for Research and Development in Mathematics and Applications(CIDMA)the Portuguese Foundation for Science and Technology(FCT),within project UID/MAT/04106/2013
文摘Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether's symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.
基金co-supported by the National Key Project of China(No.GJXM92579)the National Natural Science Foundation of China(Nos.92052203,61903178 and61906081)。
文摘Inverse design has long been an efficient and powerful design tool in the aircraft industry.In this paper,a novel inverse design method for supercritical airfoils is proposed based on generative models in deep learning.A Conditional Variational Auto Encoder(CVAE)and an integrated generative network CVAE-GAN that combines the CVAE with the Wasserstein Generative Adversarial Networks(WGAN),are conducted as generative models.They are used to generate target wall Mach distributions for the inverse design that matches specified features,such as locations of suction peak,shock and aft loading.Qualitative and quantitative results show that both adopted generative models can generate diverse and realistic wall Mach number distributions satisfying the given features.The CVAE-GAN model outperforms the CVAE model and achieves better reconstruction accuracies for all the samples in the dataset.Furthermore,a deep neural network for nonlinear mapping is adopted to obtain the airfoil shape corresponding to the target wall Mach number distribution.The performances of the designed deep neural network are fully demonstrated and a smoothness measurement is proposed to quantify small oscillations in the airfoil surface,proving the authenticity and accuracy of the generated airfoil shapes.
文摘In this work, a new class of variational inclusion involving T-accretive operators in Banach spaces is introduced and studied. New iterative algorithms for stability for their class of variational inclusions and its convergence results are established.
基金Supported by the Natural Science Foundation of Henan Province（162300410031） Supported by the Excellent Youth Program of the Basic Research Operating Expenses Program of Henan Province （yqpy20140039）
文摘In this paper, a new variational formulation for a reaction-diffusion problem in broken Sobolev space is proposed. And the new formulation in the broken Sobolev space will be proved that it is well-posed and equivalent to the standard Galerkin variational formulation. The method will be helpful to easily solve the original partial differential equation numerically. And the method is novel and interesting, which can be used to deal with some complicated problem, such as the low regularity problem, the differential-integral problem and so on.
基金National Natural Science Foundation of China ( No. 11171062 ) Natural Science Foundation for the Youth,China ( No.11101077) Innovation Program of Shanghai Municipal Education Commission,China ( No. 12ZZ063)
文摘One existence integral condition was obtained for the adapted solution of the general backward stochastic differential equations(BSDEs). Then by solving the integral constraint condition, and using a limit procedure, a new approach method is proposed and the existence of the solution was proved for the BSDEs if the diffusion coefficients satisfy the locally Lipschitz condition. In the special case the solution was a Brownian bridge. The uniqueness is also considered in the meaning of "F0-integrable equivalent class" . The new approach method would give us an efficient way to control the main object instead of the "noise".
文摘In this paper,through the use of image space analysis,optimality conditions for a class of variational inequalities with cone constraints are proposed.By virtue of the nonlinear scalarization function,known as the Gerstewitz function,three nonlinear weak separation functions,two nonlinear regular weak separation functions and a nonlinear strong separation function are introduced.According to nonlinearseparation functions,some optimality conditions of the weak and strong alternative for variational inequalities with cone constraints are derived.
文摘To reveal the multivariate relationships between man-made and meteorological factors on dust storm frequency, the LUCC data, NDVI remote sensing data and meteorological data for the period of 1983-2013 were combined with dust storm frequency data, and the possible impacts of meteorological and anthropogenic factors on dust storm frequency were analyzed by using regression analysis and PCA (Principal Component Analysis). Results show that the inter-annual dust storm frequency increased gradually. In particular, an increasing trend in recent years, after 2009, is conspicuous. The monthly frequency of dust storms shows higher values between the months of February and May, with the highest mean number of events occurring in April, which accounts for 29% of the annual dust storm frequency. The annual dust storm frequency is positively correlated with wind speed and negatively correlated with precipitation;the monthly dust storm frequency is positively correlated with wind speed, but no significant correlation can be found with precipitation. The relationship between temperature and dust storms is not simply linear, however, a certain correlation with an unremarkable statistical significance can be found between them. Human activities also affect the dynamics of dust storms indirectly via changing vegetation coverage and direct dust emissions. The multivariate analysis further confirmed the association between dust storm frequency and meteorological factors and NDVI. The high loadings of dust storm frequency, wind speed, precipitation and NDVI on a PC indicate that the increased precipitation and NDVI will decrease dust storm frequency, and increased wind speed will increase dust storm frequency.
基金supported by the National Key R&D Program of China(Grant No.2019YFA0308700)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301500)。
文摘The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or scheduling,and integer partitions.An accurate search algorithm with polynomial time complexity has not been found,which makes it challenging to be solved on classical computers.To effectively solve this problem,we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk.The proposed model needs only n qubits to encode 2ndimensional search space,which can effectively save the encoding quantum resources.The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise,and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era.We investigate the effects of the scalability,the variational ansatz type,the variational depth,and noise on the model.Moreover,we also discuss the performance of the model under different conditional values at risk.Through computer simulation,the scale can reach more than nine qubits.By selecting the noise type,we construct simulators with different QVs and study the performance of the model with them.In addition,we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem.This model provides a new perspective for solving the subset sum problem.
基金Project supported by the National Natural Science Foundation of China(Nos.10902077,11172209, and 10572031)
文摘A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.
基金the National Natural Science Foundation of China(No.19971002)
文摘The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions problem is proposed, and some desirable properties of the merit function are obtained. Through the merit function, the original problem is reformulated as minimization with simple constraints. Then, the authors show that any stationary point of the optimization problem is a solution of the original problem. Finally, a descent algorithm is presented for the optimization problem, and global convergence is shown.
文摘The variational analysis of the Pseudo-potential function-vortex-potential function model, a new mathematical model, was developed and by which the flow field with transonic speed and curl was decided, and different sorts of the variational principle for vortex potential function were established by transforming the original equation for vortex-function, the boundary conditions for vortex-potential function was raised.
基金Supported by the National Natural Science Foundation of China(11801499)。
文摘In this article we study the existence of solutions for the Dirac systems with the chirality boundary condition.Using an analytic framework of proper products of fractional Sobolev spaces,the solutions existence results of the coupled Dirac systems are obtained for nonlinearity with superquadratic growth rates.The results obtained by GONG and LU(2017)are extended to the case of chiral boundary condition.
