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
A new approach that bounds the largest eigenvalue of 3 × 3 correlation matrices is presented. Optimal bounds by given determinant and trace of the squared correlation matrix are derived and shown to be more strin...A new approach that bounds the largest eigenvalue of 3 × 3 correlation matrices is presented. Optimal bounds by given determinant and trace of the squared correlation matrix are derived and shown to be more stringent than the optimal bounds by Wolkowicz and Styan in specific cases.展开更多
For the expected value formulation of stochastic linear complementarity problem, we establish modulus-based matrix splitting iteration methods. The convergence of the new methods is discussed when the coefficient matr...For the expected value formulation of stochastic linear complementarity problem, we establish modulus-based matrix splitting iteration methods. The convergence of the new methods is discussed when the coefficient matrix is a positive definite matrix or a positive semi-definite matrix, respectively. The advantages of the new methods are that they can solve the large scale stochastic linear complementarity problem, and spend less computational time. Numerical results show that the new methods are efficient and suitable for solving the large scale problems.展开更多
In this paper, we further generalize the technique for constructing the normal （or pos- itive definite） and skew-Hermitian splitting iteration method for solving large sparse non- Hermitian positive definite system ...In this paper, we further generalize the technique for constructing the normal （or pos- itive definite） and skew-Hermitian splitting iteration method for solving large sparse non- Hermitian positive definite system of linear equations. By introducing a new splitting, we establish a class of efficient iteration methods, called positive definite and semi-definite splitting （PPS） methods, and prove that the sequence produced by the PPS method con- verges unconditionally to the unique solution of the system. Moreover, we propose two kinds of typical practical choices of the PPS method and study the upper bound of the spectral radius of the iteration matrix. In addition, we show the optimal parameters such that the spectral radius achieves the minimum under certain conditions. Finally, some numerical examples are given to demonstrate the effectiveness of the considered methods.展开更多
In this paper, we consider two different formulations （one is smooth and the other one is nonsmooth） for solving linear matrix inequalities （LMIs）, an important class of semidefinite programming （SDP）, under a c...In this paper, we consider two different formulations （one is smooth and the other one is nonsmooth） for solving linear matrix inequalities （LMIs）, an important class of semidefinite programming （SDP）, under a certain Slater constraint qualification assumption. We then propose two first-order methods, one based on subgradient method and the other based on Nesterov＇s optimal method, and show that they converge linearly for solving these formulations. Moreover, we introduce an accelerated prox-level method which converges linearly uniformly for both smooth and non-smooth problems without requiring the input of any problem parameters. Finally, we consider a special case of LMIs, i.e., linear system of inequalities, and show that a linearly convergent algorithm can be obtained under a much weaker assumption.展开更多
无线传感网络WSNs(Wireless Sensor Networks)的定位精度严重受到环境的影响,尤其是高噪声电平和非视距连接的恶劣环境,定位精度急剧下降。为此,提出基于半定规划的恶劣环境下定位修正算法,记为ESDP_O算法。该修正算法以半定规划ESDP(Ed...无线传感网络WSNs(Wireless Sensor Networks)的定位精度严重受到环境的影响,尤其是高噪声电平和非视距连接的恶劣环境,定位精度急剧下降。为此,提出基于半定规划的恶劣环境下定位修正算法,记为ESDP_O算法。该修正算法以半定规划ESDP(Edge-Semi-Definite Programming)算法为基础,旨在提高定位精度,并降低算法复杂性,进而减少定位时间。ESDP_O算法通过引用抖动矩阵,对ESDP算法进行修改,提高了算法在恶劣环境的健壮性。同时,ESDP_O算法通过寻找低秩解,减少高噪声和非视距偏差。仿真结果表明,在高噪声和非视距NLOS(Non Line of Sight)的恶劣环境下,ESDP_O算法的定位精度优于基于同类算法,并且降低了定位的复杂度。展开更多
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.
文摘A new approach that bounds the largest eigenvalue of 3 × 3 correlation matrices is presented. Optimal bounds by given determinant and trace of the squared correlation matrix are derived and shown to be more stringent than the optimal bounds by Wolkowicz and Styan in specific cases.
文摘For the expected value formulation of stochastic linear complementarity problem, we establish modulus-based matrix splitting iteration methods. The convergence of the new methods is discussed when the coefficient matrix is a positive definite matrix or a positive semi-definite matrix, respectively. The advantages of the new methods are that they can solve the large scale stochastic linear complementarity problem, and spend less computational time. Numerical results show that the new methods are efficient and suitable for solving the large scale problems.
文摘In this paper, we further generalize the technique for constructing the normal （or pos- itive definite） and skew-Hermitian splitting iteration method for solving large sparse non- Hermitian positive definite system of linear equations. By introducing a new splitting, we establish a class of efficient iteration methods, called positive definite and semi-definite splitting （PPS） methods, and prove that the sequence produced by the PPS method con- verges unconditionally to the unique solution of the system. Moreover, we propose two kinds of typical practical choices of the PPS method and study the upper bound of the spectral radius of the iteration matrix. In addition, we show the optimal parameters such that the spectral radius achieves the minimum under certain conditions. Finally, some numerical examples are given to demonstrate the effectiveness of the considered methods.
文摘In this paper, we consider two different formulations （one is smooth and the other one is nonsmooth） for solving linear matrix inequalities （LMIs）, an important class of semidefinite programming （SDP）, under a certain Slater constraint qualification assumption. We then propose two first-order methods, one based on subgradient method and the other based on Nesterov＇s optimal method, and show that they converge linearly for solving these formulations. Moreover, we introduce an accelerated prox-level method which converges linearly uniformly for both smooth and non-smooth problems without requiring the input of any problem parameters. Finally, we consider a special case of LMIs, i.e., linear system of inequalities, and show that a linearly convergent algorithm can be obtained under a much weaker assumption.
文摘无线传感网络WSNs(Wireless Sensor Networks)的定位精度严重受到环境的影响,尤其是高噪声电平和非视距连接的恶劣环境,定位精度急剧下降。为此,提出基于半定规划的恶劣环境下定位修正算法,记为ESDP_O算法。该修正算法以半定规划ESDP(Edge-Semi-Definite Programming)算法为基础,旨在提高定位精度,并降低算法复杂性,进而减少定位时间。ESDP_O算法通过引用抖动矩阵,对ESDP算法进行修改,提高了算法在恶劣环境的健壮性。同时,ESDP_O算法通过寻找低秩解,减少高噪声和非视距偏差。仿真结果表明,在高噪声和非视距NLOS(Non Line of Sight)的恶劣环境下,ESDP_O算法的定位精度优于基于同类算法,并且降低了定位的复杂度。
