For an arbitrary tensor(multi-index array) with linear constraints at each direction,it is proved that the factors of any minimal canonical tensor approximation to this tensor satisfy the same linear constraints for t...For an arbitrary tensor(multi-index array) with linear constraints at each direction,it is proved that the factors of any minimal canonical tensor approximation to this tensor satisfy the same linear constraints for the corresponding directions.展开更多
We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. ...We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a given network and introduce a time discretization thereof. We then study the well-posedness of the corresponding time-discrete optimal control problem. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a non-overlapping domain decomposition of the semi-linear elliptic optimal control problem on the graph into local problems on a small part of the network, ultimately on a single edge.展开更多
提出了在大规模安全约束最优潮流(Security-constrained Optimal Power Flow,SCOPF)问题下应用近似牛顿方向(Approximate Newton Directions,AND)分解协调算法。该算法利用近似牛顿方向直接对原问题Karush-Kuhn-Tucker(KKT)条件解耦的思...提出了在大规模安全约束最优潮流(Security-constrained Optimal Power Flow,SCOPF)问题下应用近似牛顿方向(Approximate Newton Directions,AND)分解协调算法。该算法利用近似牛顿方向直接对原问题Karush-Kuhn-Tucker(KKT)条件解耦的思想,将校正性安全约束最优潮流问题分解为一个正常运行状态子问题和N个故障状态子问题,N为预想故障数。分解的每个子问题只迭代1次而不用求其最优解,避免了参数的人为调整,极大地提高了计算效率。对1 047节点424个预想故障、高达4 559 128个原-对偶变量的实际系统进行计算,结果表明所提算法具有良好的适应性和稳定性,不仅显著地减少了占用内存,而且在串行求解时CPU时间下降了3~6倍,在并行计算条件下可获得10~30倍甚至200倍以上的加速比,并保证所得最优目标值与准确值的误差在10^(-8)以下,确保了分解协调结果的最优性。展开更多
基金supported by the Russian Fund for Basic Research (RFBR grant 08-01-00115,RFBR/DFG grant 09-01-91332,RFBR grant 09-01-12058)Priority Research Programme of Department of Mathematical Sciences of Russian Academy of Sciences
文摘For an arbitrary tensor(multi-index array) with linear constraints at each direction,it is proved that the factors of any minimal canonical tensor approximation to this tensor satisfy the same linear constraints for the corresponding directions.
文摘We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a given network and introduce a time discretization thereof. We then study the well-posedness of the corresponding time-discrete optimal control problem. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a non-overlapping domain decomposition of the semi-linear elliptic optimal control problem on the graph into local problems on a small part of the network, ultimately on a single edge.
文摘提出了在大规模安全约束最优潮流(Security-constrained Optimal Power Flow,SCOPF)问题下应用近似牛顿方向(Approximate Newton Directions,AND)分解协调算法。该算法利用近似牛顿方向直接对原问题Karush-Kuhn-Tucker(KKT)条件解耦的思想,将校正性安全约束最优潮流问题分解为一个正常运行状态子问题和N个故障状态子问题,N为预想故障数。分解的每个子问题只迭代1次而不用求其最优解,避免了参数的人为调整,极大地提高了计算效率。对1 047节点424个预想故障、高达4 559 128个原-对偶变量的实际系统进行计算,结果表明所提算法具有良好的适应性和稳定性,不仅显著地减少了占用内存,而且在串行求解时CPU时间下降了3~6倍,在并行计算条件下可获得10~30倍甚至200倍以上的加速比,并保证所得最优目标值与准确值的误差在10^(-8)以下,确保了分解协调结果的最优性。
