Firstly,this paper proposes a generalized log-determinant optimization model with the purpose of estimating the high-dimensional sparse inverse covariance matrices.Under the normality assumption,the zero components in...Firstly,this paper proposes a generalized log-determinant optimization model with the purpose of estimating the high-dimensional sparse inverse covariance matrices.Under the normality assumption,the zero components in the inverse covariance matrices represent the conditional independence between pairs of variables given all the other variables.The generalized model considered in this study,because of the setting of the eigenvalue bounded constraints,covers a large number of existing estimators as special cases.Secondly,rather than directly tracking the challenging optimization problem,this paper uses a couple of alternating direction methods of multipliers(ADMM)to solve its dual model where 5 separable structures are contained.The first implemented algorithm is based on a single Gauss–Seidel iteration,but it does not necessarily converge theoretically.In contrast,the second algorithm employs the symmetric Gauss–Seidel(sGS)based ADMM which is equivalent to the 2-block iterative scheme from the latest sGS decomposition theorem.Finally,we do numerical simulations using the synthetic data and the real data set which show that both algorithms are very effective in estimating high-dimensional sparse inverse covariance matrix.展开更多
In this paper, a modified limited memory BFGS method for solving large-scale unconstrained optimization problems is proposed. A remarkable feature of the proposed method is that it possesses global convergence propert...In this paper, a modified limited memory BFGS method for solving large-scale unconstrained optimization problems is proposed. A remarkable feature of the proposed method is that it possesses global convergence property without convexity assumption on the objective function. Under some suitable conditions, the global convergence of the proposed method is proved. Some numerical results are reported which illustrate that the proposed method is efficient.展开更多
基金the National Natural Science Foundation of China(No.11971149).
文摘Firstly,this paper proposes a generalized log-determinant optimization model with the purpose of estimating the high-dimensional sparse inverse covariance matrices.Under the normality assumption,the zero components in the inverse covariance matrices represent the conditional independence between pairs of variables given all the other variables.The generalized model considered in this study,because of the setting of the eigenvalue bounded constraints,covers a large number of existing estimators as special cases.Secondly,rather than directly tracking the challenging optimization problem,this paper uses a couple of alternating direction methods of multipliers(ADMM)to solve its dual model where 5 separable structures are contained.The first implemented algorithm is based on a single Gauss–Seidel iteration,but it does not necessarily converge theoretically.In contrast,the second algorithm employs the symmetric Gauss–Seidel(sGS)based ADMM which is equivalent to the 2-block iterative scheme from the latest sGS decomposition theorem.Finally,we do numerical simulations using the synthetic data and the real data set which show that both algorithms are very effective in estimating high-dimensional sparse inverse covariance matrix.
基金Supported by National Natural Science Foundation of China(Grant11001075,11161003)Post-doctoral Foundation of China grant 20090461094the Natural Science Foundation of Henan Province Eduction Department grant 2010B110004
文摘In this paper, a modified limited memory BFGS method for solving large-scale unconstrained optimization problems is proposed. A remarkable feature of the proposed method is that it possesses global convergence property without convexity assumption on the objective function. Under some suitable conditions, the global convergence of the proposed method is proved. Some numerical results are reported which illustrate that the proposed method is efficient.
