This paper aims at solving the linear-quadratic optimal control problems(LQOCP)for time-varying descriptor systems in a real Hilbert space.By using the Moore-Penrose inverse theory and space decomposition technique,th...This paper aims at solving the linear-quadratic optimal control problems(LQOCP)for time-varying descriptor systems in a real Hilbert space.By using the Moore-Penrose inverse theory and space decomposition technique,the descriptor system can be rewritten as a new differential-algebraic equation(DAE),and then some novel sufficient conditions for the solvability of LQOCP are obtained.Especially,the methods proposed in this work are simpler and easier to verify and compute,and can solve LQOCP without the range inclusion condition.In addition,some numerical examples are shown to verify the results obtained.展开更多
Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which...Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which can be applied to some nonuniformly elliptic problems.展开更多
In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linea...In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.展开更多
Maintaining population diversity is an important task in the multimodal multi-objective optimization.Although the zoning search(ZS)can improve the diversity in the decision space,assigning the same computational costs...Maintaining population diversity is an important task in the multimodal multi-objective optimization.Although the zoning search(ZS)can improve the diversity in the decision space,assigning the same computational costs to each search subspace may be wasteful when computational resources are limited,especially on imbalanced problems.To alleviate the above-mentioned issue,a zoning search with adaptive resource allocating(ZS-ARA)method is proposed in the current study.In the proposed ZS-ARA,the entire search space is divided into many subspaces to preserve the diversity in the decision space and to reduce the problem complexity.Moreover,the computational resources can be automatically allocated among all the subspaces.The ZS-ARA is compared with seven algorithms on two different types of multimodal multi-objective problems(MMOPs),namely,balanced and imbalanced MMOPs.The results indicate that,similarly to the ZS,the ZS-ARA achieves high performance with the balanced MMOPs.Also,it can greatly assist a“regular”algorithm in improving its performance on the imbalanced MMOPs,and is capable of allocating the limited computational resources dynamically.展开更多
This paper shows that every non-separable hereditarily indecomposable Banach space admits an equivalent strictly convex norm, but its bi-dual can never have such a one; consequently, every non-separable hereditarily i...This paper shows that every non-separable hereditarily indecomposable Banach space admits an equivalent strictly convex norm, but its bi-dual can never have such a one; consequently, every non-separable hereditarily indecomposable Banach space has no equivalent locally uniformly convex norm.展开更多
When the rate of a symmetric second-order symmetric tensor is discussed,the spin of the principal axis is involved.This paper proposes a method to establish the basis-free expression of the spin in terms of tensor and...When the rate of a symmetric second-order symmetric tensor is discussed,the spin of the principal axis is involved.This paper proposes a method to establish the basis-free expression of the spin in terms of tensor and its rate by making use of the tensor function representation theorem.The proposed method is simple and the expression of the spin established is compact.To obtain the rate of the isotropic function of a second-order symmetric tensor,the fourth-order tangent tensor needs to be derived,which is the derivative of the tensor function to the second-order tensor.By decomposing the second-order symmetric tensor space into two orthogonal subspaces,the closed-form fourth-order tangent tensor is decomposed into two parts,which are linear mappings in these two orthogonal subspaces,respectively.These two linear mappings are derived in an extremely simple way.Finally,the method proposed in this paper is applied to obtain the expression of the relationship between material logarithmic strain rate and deformation rate.The whole process is simple and avoids tedious operations.展开更多
基金supported by the National Natural Science Foundation of China(11961052,62173355)the Natural Science Foundation of Inner Mongolia(2021MS01006)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(NMGIRT2317)。
文摘This paper aims at solving the linear-quadratic optimal control problems(LQOCP)for time-varying descriptor systems in a real Hilbert space.By using the Moore-Penrose inverse theory and space decomposition technique,the descriptor system can be rewritten as a new differential-algebraic equation(DAE),and then some novel sufficient conditions for the solvability of LQOCP are obtained.Especially,the methods proposed in this work are simpler and easier to verify and compute,and can solve LQOCP without the range inclusion condition.In addition,some numerical examples are shown to verify the results obtained.
基金the National Natural Science Foundation of China (No.19771034).
文摘Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which can be applied to some nonuniformly elliptic problems.
基金supported by the NNSF of China(12261065)the NSF of Inner Mongolia(2022MS01005)+1 种基金the Basic Science Research Fund of the Universities Directly under the Inner Mongolia Autonomous Re-gion(JY20220084)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(NMGIRT2317).
文摘In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.
基金This work was partially supported by the Shandong Joint Fund of the National Nature Science Foundation of China(U2006228)the National Nature Science Foundation of China(61603244).
文摘Maintaining population diversity is an important task in the multimodal multi-objective optimization.Although the zoning search(ZS)can improve the diversity in the decision space,assigning the same computational costs to each search subspace may be wasteful when computational resources are limited,especially on imbalanced problems.To alleviate the above-mentioned issue,a zoning search with adaptive resource allocating(ZS-ARA)method is proposed in the current study.In the proposed ZS-ARA,the entire search space is divided into many subspaces to preserve the diversity in the decision space and to reduce the problem complexity.Moreover,the computational resources can be automatically allocated among all the subspaces.The ZS-ARA is compared with seven algorithms on two different types of multimodal multi-objective problems(MMOPs),namely,balanced and imbalanced MMOPs.The results indicate that,similarly to the ZS,the ZS-ARA achieves high performance with the balanced MMOPs.Also,it can greatly assist a“regular”algorithm in improving its performance on the imbalanced MMOPs,and is capable of allocating the limited computational resources dynamically.
基金Research supported by NSFC(Grant No.10471114 and No.10471025)
文摘This paper shows that every non-separable hereditarily indecomposable Banach space admits an equivalent strictly convex norm, but its bi-dual can never have such a one; consequently, every non-separable hereditarily indecomposable Banach space has no equivalent locally uniformly convex norm.
文摘When the rate of a symmetric second-order symmetric tensor is discussed,the spin of the principal axis is involved.This paper proposes a method to establish the basis-free expression of the spin in terms of tensor and its rate by making use of the tensor function representation theorem.The proposed method is simple and the expression of the spin established is compact.To obtain the rate of the isotropic function of a second-order symmetric tensor,the fourth-order tangent tensor needs to be derived,which is the derivative of the tensor function to the second-order tensor.By decomposing the second-order symmetric tensor space into two orthogonal subspaces,the closed-form fourth-order tangent tensor is decomposed into two parts,which are linear mappings in these two orthogonal subspaces,respectively.These two linear mappings are derived in an extremely simple way.Finally,the method proposed in this paper is applied to obtain the expression of the relationship between material logarithmic strain rate and deformation rate.The whole process is simple and avoids tedious operations.