this paper,we propose an infeasible-interior-point method,based on a new wide neighborhood of the central path,for linear complementarity problems over symmetric cones with the Cartesian P_(∗)(κ)-property.The converg...this paper,we propose an infeasible-interior-point method,based on a new wide neighborhood of the central path,for linear complementarity problems over symmetric cones with the Cartesian P_(∗)(κ)-property.The convergence is shown for commutative class of search directions.Moreover,we analyze the algorithm and obtain the complexity bounds,which coincide with the best-known results for the Cartesian P_(∗)(κ)-SCLCPs.Some numerical tests are reported to illustrate our theoretical results.展开更多
This paper presents a class of primal-dual path-following interior-point algorithms for symmetric cone programming(SCP)based on wide neighborhoods and new directions with a parameterθ.When the parameterθ=1,the direc...This paper presents a class of primal-dual path-following interior-point algorithms for symmetric cone programming(SCP)based on wide neighborhoods and new directions with a parameterθ.When the parameterθ=1,the direction is exactly the classical Newton direction.When the parameterθis independent of the rank of the associated Euclidean Jordan algebra,the algorithm terminates in at most O(κr logε−1)iterations,which coincides with the best known iteration bound for the classical wide neighborhood algorithms.When the parameterθ=√n/βτand Nesterov–Todd search direction is used,the algorithm has O(√r logε−1)iteration complexity,the best iteration complexity obtained so far by any interior-point method for solving SCP.To our knowledge,this is the first time that a class of interior-point algorithms including the classical wide neighborhood path-following algorithm is proposed and analyzed over symmetric cone.展开更多
In this paper,we present an infeasible-interior-point algorithm,based on a new wide neighborhood for symmetric cone programming.We treat the classical Newton direction as the sum of two other directions,and equip them...In this paper,we present an infeasible-interior-point algorithm,based on a new wide neighborhood for symmetric cone programming.We treat the classical Newton direction as the sum of two other directions,and equip them with different step sizes.We prove the complexity bound of the new algorithm for the Nesterov-Todd(NT)direction,and the xs and sx directions.The complexity bounds obtained here are the same as small neighborhood infeasible-interior-point algorithms over symmetric cones.展开更多
In this paper,we propose an interior-point algorithm based on a wide neighborhood for convex quadratic semidefinite optimization problems.Using the Nesterov–Todd direction as the search direction,we prove the converg...In this paper,we propose an interior-point algorithm based on a wide neighborhood for convex quadratic semidefinite optimization problems.Using the Nesterov–Todd direction as the search direction,we prove the convergence analysis and obtain the polynomial complexity bound of the proposed algorithm.Although the algorithm belongs to the class of large-step interior-point algorithms,its complexity coincides with the best iteration bound for short-step interior-point algorithms.The algorithm is also implemented to demonstrate that it is efficient.展开更多
For large-scale networked plant-wide systems composed by physically(or geographically) divided subsystems, only limited information is available for local controllers on account of region and communication restriction...For large-scale networked plant-wide systems composed by physically(or geographically) divided subsystems, only limited information is available for local controllers on account of region and communication restrictions. Concerning the optimal control problem of such subsystems, a neighbor-based distributed model predictive control(NDMPC) strategy is presented to improve the global system performance. In this scheme, the performance index of local subsystems and that of its neighbors are minimized together in the determination of the optimal control input, which makes the local control decision also beneficial to its neighboring subsystems and further contributes to improving the convergence and control performance of overall system.The stability of the closed-loop system is proved. Moreover, the parameter designing method for distributed synthesis is provided.Finally, the simulation results illustrate the main characteristics and effectiveness of the proposed control scheme.展开更多
基金The authors were partially supported by the Center of Excellence for Mathematics,University of Shahrekord,Shahrekord,Iran.
文摘this paper,we propose an infeasible-interior-point method,based on a new wide neighborhood of the central path,for linear complementarity problems over symmetric cones with the Cartesian P_(∗)(κ)-property.The convergence is shown for commutative class of search directions.Moreover,we analyze the algorithm and obtain the complexity bounds,which coincide with the best-known results for the Cartesian P_(∗)(κ)-SCLCPs.Some numerical tests are reported to illustrate our theoretical results.
基金the National Natural Science Foundation of China(No.11471102)the Key Basic Research Foundation of the Higher Education Institutions of Henan Province(No.16A110012)。
文摘This paper presents a class of primal-dual path-following interior-point algorithms for symmetric cone programming(SCP)based on wide neighborhoods and new directions with a parameterθ.When the parameterθ=1,the direction is exactly the classical Newton direction.When the parameterθis independent of the rank of the associated Euclidean Jordan algebra,the algorithm terminates in at most O(κr logε−1)iterations,which coincides with the best known iteration bound for the classical wide neighborhood algorithms.When the parameterθ=√n/βτand Nesterov–Todd search direction is used,the algorithm has O(√r logε−1)iteration complexity,the best iteration complexity obtained so far by any interior-point method for solving SCP.To our knowledge,this is the first time that a class of interior-point algorithms including the classical wide neighborhood path-following algorithm is proposed and analyzed over symmetric cone.
基金the National Natural Science Foundation of China(Nos.11471102,11426091,and 61179040)the Natural Science Foundation of Henan University of Science and Technology(No.2014QN039)Key Basic Research Foundation of the Higher Education Institutions of Henan Province(No.16A110012).
文摘In this paper,we present an infeasible-interior-point algorithm,based on a new wide neighborhood for symmetric cone programming.We treat the classical Newton direction as the sum of two other directions,and equip them with different step sizes.We prove the complexity bound of the new algorithm for the Nesterov-Todd(NT)direction,and the xs and sx directions.The complexity bounds obtained here are the same as small neighborhood infeasible-interior-point algorithms over symmetric cones.
文摘In this paper,we propose an interior-point algorithm based on a wide neighborhood for convex quadratic semidefinite optimization problems.Using the Nesterov–Todd direction as the search direction,we prove the convergence analysis and obtain the polynomial complexity bound of the proposed algorithm.Although the algorithm belongs to the class of large-step interior-point algorithms,its complexity coincides with the best iteration bound for short-step interior-point algorithms.The algorithm is also implemented to demonstrate that it is efficient.
基金supported by the National Nature Science Foundation of China (61590924,61673273,61833012)
文摘For large-scale networked plant-wide systems composed by physically(or geographically) divided subsystems, only limited information is available for local controllers on account of region and communication restrictions. Concerning the optimal control problem of such subsystems, a neighbor-based distributed model predictive control(NDMPC) strategy is presented to improve the global system performance. In this scheme, the performance index of local subsystems and that of its neighbors are minimized together in the determination of the optimal control input, which makes the local control decision also beneficial to its neighboring subsystems and further contributes to improving the convergence and control performance of overall system.The stability of the closed-loop system is proved. Moreover, the parameter designing method for distributed synthesis is provided.Finally, the simulation results illustrate the main characteristics and effectiveness of the proposed control scheme.
