A modified exact Jacobian semidefinite programming(SDP)relaxation method is proposed in this paper to solve the Celis-Dennis-Tapia(CDT)problem using the Jacobian matrix of objective and constraining polynomials.In the...A modified exact Jacobian semidefinite programming(SDP)relaxation method is proposed in this paper to solve the Celis-Dennis-Tapia(CDT)problem using the Jacobian matrix of objective and constraining polynomials.In the modified relaxation problem,the number of introduced constraints and the lowest relaxation order decreases significantly.At the same time,the finite convergence property is guaranteed.In addition,the proposed method can be applied to the quadratically constrained problem with two quadratic constraints.Moreover,the efficiency of the proposed method is verified by numerical experiments.展开更多
Time-differences-of-arrival （TDOA） and gain-ratios-of- arrival （GROA） measurements are used to determine the passive source location. Based on the measurement models, the con- strained weighted least squares （CWL...Time-differences-of-arrival （TDOA） and gain-ratios-of- arrival （GROA） measurements are used to determine the passive source location. Based on the measurement models, the con- strained weighted least squares （CWLS） estimator is presented. Due to the nonconvex nature of the CWLS problem, it is difficult to obtain its globally optimal solution. However, according to the semidefinite relaxation, the CWLS problem can be relaxed as a convex semidefinite programming problem （SDP）, which can be solved by using modern convex optimization algorithms. Moreover, this relaxation can be proved to be tight, i.e., the SDP solves the relaxed CWLS problem, and this hence guarantees the good per- formance of the proposed method. Furthermore, this method is extended to solve the localization problem with sensor position errors. Simulation results corroborate the theoretical results and the good performance of the proposed method.展开更多
We consider the Max Directed 3-Section problem,which is closely connected to other well-known graph partition problems,such as Max Cut and Max Bisection.Given an arc-weighted directed graph,the goal of the Max Directe...We consider the Max Directed 3-Section problem,which is closely connected to other well-known graph partition problems,such as Max Cut and Max Bisection.Given an arc-weighted directed graph,the goal of the Max Directed 3-Section problem is to partition the vertex set into three disjoint subsets with equal size,while maximizing the total weight of arcs crossing different vertex subsets.By combining the Lasserre hierarchy with the random hyperplane rounding strategy,we propose a polynomial-time algorithm with approximation ratio of 0.489.展开更多
The four-parameter lag-lead compensator design has received much attention in the last two decades. However, most approaches have been either trial-and-error or only for special cases. This paper presents a non-trial-...The four-parameter lag-lead compensator design has received much attention in the last two decades. However, most approaches have been either trial-and-error or only for special cases. This paper presents a non-trial-and-error design method for four-parameter lag-lead compensators. Here, the compensator design problem is formulated into a polynomial function optimization problem and solved by using the recently developed sum-of-squares （SOS） techniques. This result not only provides a useful design method but also shows the power of the SOS techniques.展开更多
基金Fundamental Research Funds for the Central Universities,China(No.2232019D3-38)Shanghai Sailing Program,China(No.22YF1400900)。
文摘A modified exact Jacobian semidefinite programming(SDP)relaxation method is proposed in this paper to solve the Celis-Dennis-Tapia(CDT)problem using the Jacobian matrix of objective and constraining polynomials.In the modified relaxation problem,the number of introduced constraints and the lowest relaxation order decreases significantly.At the same time,the finite convergence property is guaranteed.In addition,the proposed method can be applied to the quadratically constrained problem with two quadratic constraints.Moreover,the efficiency of the proposed method is verified by numerical experiments.
基金supported by the National Natural Science Foundation of China(61201282)the Science and Technology on Communication Information Security Control Laboratory Foundation(9140C130304120C13064)
文摘Time-differences-of-arrival （TDOA） and gain-ratios-of- arrival （GROA） measurements are used to determine the passive source location. Based on the measurement models, the con- strained weighted least squares （CWLS） estimator is presented. Due to the nonconvex nature of the CWLS problem, it is difficult to obtain its globally optimal solution. However, according to the semidefinite relaxation, the CWLS problem can be relaxed as a convex semidefinite programming problem （SDP）, which can be solved by using modern convex optimization algorithms. Moreover, this relaxation can be proved to be tight, i.e., the SDP solves the relaxed CWLS problem, and this hence guarantees the good per- formance of the proposed method. Furthermore, this method is extended to solve the localization problem with sensor position errors. Simulation results corroborate the theoretical results and the good performance of the proposed method.
基金supported by the National Natural Science Foundation of China(Nos.12271259 and 12301414)the China Scholarship Council(No.202306200014)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Nos.KYCX24_1785).
文摘We consider the Max Directed 3-Section problem,which is closely connected to other well-known graph partition problems,such as Max Cut and Max Bisection.Given an arc-weighted directed graph,the goal of the Max Directed 3-Section problem is to partition the vertex set into three disjoint subsets with equal size,while maximizing the total weight of arcs crossing different vertex subsets.By combining the Lasserre hierarchy with the random hyperplane rounding strategy,we propose a polynomial-time algorithm with approximation ratio of 0.489.
基金Supported in part by the National High-Tech Research and Development (863) Program of China (Nos.2007AA11Z215 and 2007AA11Z222)the National Key Technology Research and Development Program (No.2006CBJ18B02)
文摘The four-parameter lag-lead compensator design has received much attention in the last two decades. However, most approaches have been either trial-and-error or only for special cases. This paper presents a non-trial-and-error design method for four-parameter lag-lead compensators. Here, the compensator design problem is formulated into a polynomial function optimization problem and solved by using the recently developed sum-of-squares （SOS） techniques. This result not only provides a useful design method but also shows the power of the SOS techniques.
