In order to provide a judicious pulse waveform design required for ultra-wideband(UWB)communication to enable the UWB spectral mask compatible and coexistent with other existing wireless communication systems,a semi-d...In order to provide a judicious pulse waveform design required for ultra-wideband(UWB)communication to enable the UWB spectral mask compatible and coexistent with other existing wireless communication systems,a semi-definite programming(SDP)based pulse waveform design method for UWB radios is introduced and a further analysis is given in this paper.By using Sedumi and Yalmip toolboxes of Matlab,the procedure of solving the SDP problem is simplified.Simulation results show that this SDP based pulse waveform design method can be used to design pulses that fulfill the Federal Communications Commission(FCC)spectral mask strictly and optimize the power efficiency at the same time.This paper also analyzes the influences of the power efficiency duing to the changes of sampling interval and the number of combined pulses,and then the optimal sampling interval that maximizes the transmission power can be found.展开更多
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
It is well known that for symmetric linear programming there exists a strictly complementary solution if the primal and the dual problems are both feasible. However, this is not necessary true for symmetric or general...It is well known that for symmetric linear programming there exists a strictly complementary solution if the primal and the dual problems are both feasible. However, this is not necessary true for symmetric or general semide finite programming even if both the primal problem and its dual problem are strictly feasible. Some other properties are also concerned.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
This paper proposes an inner product Laplacian embedding algorithm based on semi-definite programming, named as IPLE algorithm. The new algorithm learns a geodesic distance-based kernel matrix by using semi-definite p...This paper proposes an inner product Laplacian embedding algorithm based on semi-definite programming, named as IPLE algorithm. The new algorithm learns a geodesic distance-based kernel matrix by using semi-definite programming under the constraints of local contraction. The criterion function is to make the neighborhood points on manifold as close as possible while the geodesic distances between those distant points are preserved. The IPLE algorithm sufficiently integrates the advantages of LE, ISOMAP and MVU algorithms. The comparison experiments on two image datasets from COIL-20 images and USPS handwritten digit images are performed by applying LE, ISOMAP, MVU and the proposed IPLE. Experimental results show that the intrinsic low-dimensional coordinates obtained by our algorithm preserve more information according to the fraction of the dominant eigenvalues and can obtain the better comprehensive performance in clustering and manifold structure.展开更多
In this paper we introduce a primal-dual potential reduction algorithm for positive semi-definite programming. Using the symetric preserving scalings for both primal and dual interior matrices, we can construct an alg...In this paper we introduce a primal-dual potential reduction algorithm for positive semi-definite programming. Using the symetric preserving scalings for both primal and dual interior matrices, we can construct an algorithm which is very similar to the primal-dual potential reduction algorithm of Huang and Kortanek [6] for linear programming. The complexity of the algorithm is either O(nlog(X0 · S0/ε) or O(nlog(X0· S0/ε) depends on the value of ρ in the primal-dual potential function, where X0 and S0 is the initial interior matrices of the positive semi-definite programming.展开更多
Received signal strength(RSS)based positioning schemes ignore the actual environmental feature that the volatility of RSS increases as signal propagation distance grows.Therefore,RSS over long distance generally has r...Received signal strength(RSS)based positioning schemes ignore the actual environmental feature that the volatility of RSS increases as signal propagation distance grows.Therefore,RSS over long distance generally has relatively large measurement error and degrades the positioning performance.To reduce the negative impact of these RSSs over long distances,a weighted semidefinite programming(WSDP)positioning scheme was proposed.The WSDP positioning scheme first assesses the signal propagation quality using the average variance of all RSS sets.Then appropriate weighting factors are set based on the variance of each RSS set,and a weighted semidefinite programming optimizer is formulated to estimate the positions of target nodes.Simulation results show that the WSDP positioning scheme can effectively improve the positioning performance.展开更多
This paper first applies the fuzzy set theory to multi-objective semi-definite program-ming （MSDP）, and proposes the fuzzy multi-objective semi-definite programming （FMSDP） model whose optimal efficient solution i...This paper first applies the fuzzy set theory to multi-objective semi-definite program-ming （MSDP）, and proposes the fuzzy multi-objective semi-definite programming （FMSDP） model whose optimal efficient solution is defined for the first time, too. By constructing a membership function, the FMSDP is translated to the MSDP. Then we prove that the optimal efficient solution of FMSDP is consistent with the efficient solution of MSDP and present the optimality condition about these programming. At last, we give an algorithm for FMSDP by introducing a new membership function and a series of transformation.展开更多
基金the National Natural Science Foundation of China (Grant No.60432040)Program for New Century Excellent Talents in University(Grant No.NCET-04-0332)
文摘In order to provide a judicious pulse waveform design required for ultra-wideband(UWB)communication to enable the UWB spectral mask compatible and coexistent with other existing wireless communication systems,a semi-definite programming(SDP)based pulse waveform design method for UWB radios is introduced and a further analysis is given in this paper.By using Sedumi and Yalmip toolboxes of Matlab,the procedure of solving the SDP problem is simplified.Simulation results show that this SDP based pulse waveform design method can be used to design pulses that fulfill the Federal Communications Commission(FCC)spectral mask strictly and optimize the power efficiency at the same time.This paper also analyzes the influences of the power efficiency duing to the changes of sampling interval and the number of combined pulses,and then the optimal sampling interval that maximizes the transmission power can be found.
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.
文摘It is well known that for symmetric linear programming there exists a strictly complementary solution if the primal and the dual problems are both feasible. However, this is not necessary true for symmetric or general semide finite programming even if both the primal problem and its dual problem are strictly feasible. Some other properties are also concerned.
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.
文摘This paper proposes an inner product Laplacian embedding algorithm based on semi-definite programming, named as IPLE algorithm. The new algorithm learns a geodesic distance-based kernel matrix by using semi-definite programming under the constraints of local contraction. The criterion function is to make the neighborhood points on manifold as close as possible while the geodesic distances between those distant points are preserved. The IPLE algorithm sufficiently integrates the advantages of LE, ISOMAP and MVU algorithms. The comparison experiments on two image datasets from COIL-20 images and USPS handwritten digit images are performed by applying LE, ISOMAP, MVU and the proposed IPLE. Experimental results show that the intrinsic low-dimensional coordinates obtained by our algorithm preserve more information according to the fraction of the dominant eigenvalues and can obtain the better comprehensive performance in clustering and manifold structure.
基金This research was partially supported by a fund from Chinese Academy of Science,and a fund from the Personal Department of the State Council.It is also sponsored by scientific research foundation for returned overseas Chinese Scholars,State Education
文摘In this paper we introduce a primal-dual potential reduction algorithm for positive semi-definite programming. Using the symetric preserving scalings for both primal and dual interior matrices, we can construct an algorithm which is very similar to the primal-dual potential reduction algorithm of Huang and Kortanek [6] for linear programming. The complexity of the algorithm is either O(nlog(X0 · S0/ε) or O(nlog(X0· S0/ε) depends on the value of ρ in the primal-dual potential function, where X0 and S0 is the initial interior matrices of the positive semi-definite programming.
基金supported by the National Natural Science Foundation of China(61871050)。
文摘Received signal strength(RSS)based positioning schemes ignore the actual environmental feature that the volatility of RSS increases as signal propagation distance grows.Therefore,RSS over long distance generally has relatively large measurement error and degrades the positioning performance.To reduce the negative impact of these RSSs over long distances,a weighted semidefinite programming(WSDP)positioning scheme was proposed.The WSDP positioning scheme first assesses the signal propagation quality using the average variance of all RSS sets.Then appropriate weighting factors are set based on the variance of each RSS set,and a weighted semidefinite programming optimizer is formulated to estimate the positions of target nodes.Simulation results show that the WSDP positioning scheme can effectively improve the positioning performance.
基金Supported by the National Natural Science Foundation of China (Grant No.10671057)
文摘This paper first applies the fuzzy set theory to multi-objective semi-definite program-ming （MSDP）, and proposes the fuzzy multi-objective semi-definite programming （FMSDP） model whose optimal efficient solution is defined for the first time, too. By constructing a membership function, the FMSDP is translated to the MSDP. Then we prove that the optimal efficient solution of FMSDP is consistent with the efficient solution of MSDP and present the optimality condition about these programming. At last, we give an algorithm for FMSDP by introducing a new membership function and a series of transformation.
