This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems...This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. （Biometrika, 72, 465472 （1983））, Shi N. Z. （J. Multivariate Anal., 50, 282-293 （1994）） and El Barmi H. and Dykstra R. （Ann. Statist., 26, 1878 1893 （1998））.展开更多
Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image ...Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image regularization methods.In recent years,matrix low-rank approximation has been successfully introduced in the image denoising problem and significant denoising effects have been achieved.Low-rank matrix minimization is an NP-hard problem and it is often replaced with the matrix’s weighted nuclear norm minimization(WNNM).The assumption that an image contains an extensive amount of self-similarity is the basis for the construction of the matrix low-rank approximation-based image denoising method.In this paper,we develop a model for image restoration using the sum of block matching matrices’weighted nuclear norm to be the regularization term in the cost function.An alternating iterative algorithm is designed to solve the proposed model and the convergence analyses of the algorithm are also presented.Numerical experiments show that the proposed method can recover the images much better than the existing regularization methods in terms of both recovered quantities and visual qualities.展开更多
The photoacoustic tomography(PAT)is a new biomedical imaging modality.It has great advantages in early diagnosis of the human disease and accurate monitoring of disease progression.In photoacoustic imaging,when a beam...The photoacoustic tomography(PAT)is a new biomedical imaging modality.It has great advantages in early diagnosis of the human disease and accurate monitoring of disease progression.In photoacoustic imaging,when a beam of short-pulsed laser illuminates the biological tissue,the photoacoustic effect leads to the emergence of acoustic waves in the tissue.The initial acoustic pressure in the tissue reveals the structures of the tissue.The purpose of the PAT reconstruction problem is to obtain the initial acoustic pressure in the tissue from the collected photoacoustic signal information.In this paper,we propose a rank minimization-based regularization model for the sparse-view photoacoustic image reconstruction problem.We design a proximal alternating iterative algorithm to solve the model and the convergence of the algorithm is demonstrated by utilizing the Kudyka-Lojasiewicz theory.The experimental results show that the proposed method is competitive with the existing state-of-the-art PAT reconstruction methods in terms of both reconstructed quantities and visual effects for the sparse-view PAT reconstruction problem.展开更多
In this paper,according to the Shamanskii technology,an alternately linearized implicit(ALI)iteration method is proposed to compute the minimal nonnegative solution to the nonsymmetric coupled algebraic Riccati equati...In this paper,according to the Shamanskii technology,an alternately linearized implicit(ALI)iteration method is proposed to compute the minimal nonnegative solution to the nonsymmetric coupled algebraic Riccati equation.Based on the ALI iteration method,we propose two modified alternately linearized implicit(MALI)iteration methods with double parameters.Further,we prove the monotone convergence of these iteration methods.Numerical examples demonstrate the effectiveness of the presented iteration methods.展开更多
This paper proposes a decentralized robust two-stage dispatch framework for multi-area integrated electric-gas systems (M-IEGSs), with the consideration of Weymouth and linepack equations of tie-pipelines. The overall...This paper proposes a decentralized robust two-stage dispatch framework for multi-area integrated electric-gas systems (M-IEGSs), with the consideration of Weymouth and linepack equations of tie-pipelines. The overall methodology includes the equivalent conversion for the robust two-stage program and the decentralized optimization for the equivalent form. To obtain a tractable and equivalent counterpart for the robust two-stage program, a quadruple-loop procedure based on the column-and-constraint generation (C&CG) and the penalty convex-concave procedure (P-CCP) algorithms is derived, resulting in a series of mixed integer second-order cone programs (MISOCPs). Then, an improved I-ADMM is proposed to realize the decentralized optimization for MISOCPs. Moreover, three acceleration methods are devised to reduce the computation burden. Simulation results validate the effectiveness of the proposed methodology and corresponding acceleration measures.展开更多
基金the National Natural Science Foundation of China (Nos.10431010,10501005)Science Foundation for Young Teachers of NENU (No.20070103)
文摘This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. （Biometrika, 72, 465472 （1983））, Shi N. Z. （J. Multivariate Anal., 50, 282-293 （1994）） and El Barmi H. and Dykstra R. （Ann. Statist., 26, 1878 1893 （1998））.
基金This work is supported by the National Natural Science Foundation of China nos.11971215 and 11571156,MOE-LCSMSchool of Mathematics and Statistics,Hunan Normal University,Changsha,Hunan 410081,China.
文摘Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image regularization methods.In recent years,matrix low-rank approximation has been successfully introduced in the image denoising problem and significant denoising effects have been achieved.Low-rank matrix minimization is an NP-hard problem and it is often replaced with the matrix’s weighted nuclear norm minimization(WNNM).The assumption that an image contains an extensive amount of self-similarity is the basis for the construction of the matrix low-rank approximation-based image denoising method.In this paper,we develop a model for image restoration using the sum of block matching matrices’weighted nuclear norm to be the regularization term in the cost function.An alternating iterative algorithm is designed to solve the proposed model and the convergence analyses of the algorithm are also presented.Numerical experiments show that the proposed method can recover the images much better than the existing regularization methods in terms of both recovered quantities and visual qualities.
基金National Natural Science Foundation of China(No.11971215)the Science and Technology Project of Gansu Province of China(No.22JR5RA391)+1 种基金the Center for Data Science of Lanzhou University,Chinathe Key Laboratory of Applied Mathematics and Complex Systems of Lanzhou University,China.
文摘The photoacoustic tomography(PAT)is a new biomedical imaging modality.It has great advantages in early diagnosis of the human disease and accurate monitoring of disease progression.In photoacoustic imaging,when a beam of short-pulsed laser illuminates the biological tissue,the photoacoustic effect leads to the emergence of acoustic waves in the tissue.The initial acoustic pressure in the tissue reveals the structures of the tissue.The purpose of the PAT reconstruction problem is to obtain the initial acoustic pressure in the tissue from the collected photoacoustic signal information.In this paper,we propose a rank minimization-based regularization model for the sparse-view photoacoustic image reconstruction problem.We design a proximal alternating iterative algorithm to solve the model and the convergence of the algorithm is demonstrated by utilizing the Kudyka-Lojasiewicz theory.The experimental results show that the proposed method is competitive with the existing state-of-the-art PAT reconstruction methods in terms of both reconstructed quantities and visual effects for the sparse-view PAT reconstruction problem.
基金National Natural Science Foundation for Youths of China(11801164)Youth Project of Hunan Provincial Education Department of China(22B0498).
文摘In this paper,according to the Shamanskii technology,an alternately linearized implicit(ALI)iteration method is proposed to compute the minimal nonnegative solution to the nonsymmetric coupled algebraic Riccati equation.Based on the ALI iteration method,we propose two modified alternately linearized implicit(MALI)iteration methods with double parameters.Further,we prove the monotone convergence of these iteration methods.Numerical examples demonstrate the effectiveness of the presented iteration methods.
文摘This paper proposes a decentralized robust two-stage dispatch framework for multi-area integrated electric-gas systems (M-IEGSs), with the consideration of Weymouth and linepack equations of tie-pipelines. The overall methodology includes the equivalent conversion for the robust two-stage program and the decentralized optimization for the equivalent form. To obtain a tractable and equivalent counterpart for the robust two-stage program, a quadruple-loop procedure based on the column-and-constraint generation (C&CG) and the penalty convex-concave procedure (P-CCP) algorithms is derived, resulting in a series of mixed integer second-order cone programs (MISOCPs). Then, an improved I-ADMM is proposed to realize the decentralized optimization for MISOCPs. Moreover, three acceleration methods are devised to reduce the computation burden. Simulation results validate the effectiveness of the proposed methodology and corresponding acceleration measures.
