In this article, we study the generalized Riemann problem for a scalar non- convex Chapman-Jouguet combustion model in a neighborhood of the origin （t 〉 0） on the （x, t） plane. We focus our attention to the pertu...In this article, we study the generalized Riemann problem for a scalar non- convex Chapman-Jouguet combustion model in a neighborhood of the origin （t 〉 0） on the （x, t） plane. We focus our attention to the perturbation on initial binding energy. The solutions are obtained constructively under the entropy conditions. It can be found that the solutions are essentially different from the corresponding Riemann solutions for some cases. Especially, two important phenomena are observed： the transition from detonation to deflagration followed by a shock, which appears in the numerical simulations [7, 27]; the transition from deflagration to detonation （DDT）, which is one of the core problems in gas dynamic combustion.展开更多
In this paper, a simplest scalar nonconvex ZND combustion model with viscosity is considered. The existence of the global solution of the Riemann problem for the combustion model is obtained by using the fixed point t...In this paper, a simplest scalar nonconvex ZND combustion model with viscosity is considered. The existence of the global solution of the Riemann problem for the combustion model is obtained by using the fixed point theorem.展开更多
In this paper, by means of combining non-probabilistic convex modeling with perturbation theory, an improvement is made on the first order approximate solution in convex models of uncertainties. Convex modeling is ext...In this paper, by means of combining non-probabilistic convex modeling with perturbation theory, an improvement is made on the first order approximate solution in convex models of uncertainties. Convex modeling is extended to largely uncertain and non-convex sets of uncertainties and the combinational convex modeling is developed. The presented method not only extends applications of convex modeling, but also improves its accuracy in uncertain problems and computational efficiency. The numerical example illustrates the efficiency of the proposed method.展开更多
The sparse phase retrieval aims to recover the sparse signal from quadratic measurements. However, the measurements are often affected by outliers and asymmetric distribution noise. This paper introduces a novel metho...The sparse phase retrieval aims to recover the sparse signal from quadratic measurements. However, the measurements are often affected by outliers and asymmetric distribution noise. This paper introduces a novel method that combines the quantile regression and the L<sub>1/2</sub>-regularizer. It is a non-convex, non-smooth, non-Lipschitz optimization problem. We propose an efficient algorithm based on the Alternating Direction Methods of Multiplier (ADMM) to solve the corresponding optimization problem. Numerous numerical experiments show that this method can recover sparse signals with fewer measurements and is robust to dense bounded noise and Laplace noise.展开更多
The new trust region subproblem with the conic model was proposed in 2005, and was divided into three different cases. The first two cases can be converted into a quadratic model or a convex problem with quadratic con...The new trust region subproblem with the conic model was proposed in 2005, and was divided into three different cases. The first two cases can be converted into a quadratic model or a convex problem with quadratic constraints, while the third one is a nonconvex problem. In this paper, first we analyze the nonconvex problem, and reduce it to two convex problems. Then we discuss some dual properties of these problems and give an algorithm for solving them. At last, we present an algorithm for solving the new trust region subproblem with the conic model and report some numerical examples to illustrate the efficiency of the algorithm.展开更多
针对传统水平集方法在分割灰度不均匀图像的过程中存在分割精度低的问题,提出一种自适应区域拟合的非均匀图像分割算法。首先构建自适应的区域拟合能量项来保留更多待分割图像局部区域内的细节信息,实现图像的准确分割;其次引入非凸正...针对传统水平集方法在分割灰度不均匀图像的过程中存在分割精度低的问题,提出一种自适应区域拟合的非均匀图像分割算法。首先构建自适应的区域拟合能量项来保留更多待分割图像局部区域内的细节信息,实现图像的准确分割;其次引入非凸正则项来平滑曲线并保护图像的边缘;然后添加能量惩罚项对水平集函数进行约束,提高算法的分割效率;最后对合成图像和真实图像进行实验验证。实验结果表明,所提算法的Dice相似系数平均值为88.62%,Jaccard相似系数平均值为79.86%,准确率平均值为92.48%,比Local Binary Fitting(LBF)、Local and Global Intensity Fitting(LGIF)、Local Pre-fitting(LPF)三种模型的总体平均值分别高18.19个百分点、16.10个百分点、13个百分点。展开更多
基金Supported by NUAA Research Funding (NS2011001)NUAA’S Scientific Fund forthe Introduction of Qualified Personal,NSFC grant 10971130+1 种基金Shanghai Leading Academic Discipline ProjectJ 50101Shanghai Municipal Education Commission of Scientific Research Innovation Project 112284
文摘In this article, we study the generalized Riemann problem for a scalar non- convex Chapman-Jouguet combustion model in a neighborhood of the origin （t 〉 0） on the （x, t） plane. We focus our attention to the perturbation on initial binding energy. The solutions are obtained constructively under the entropy conditions. It can be found that the solutions are essentially different from the corresponding Riemann solutions for some cases. Especially, two important phenomena are observed： the transition from detonation to deflagration followed by a shock, which appears in the numerical simulations [7, 27]; the transition from deflagration to detonation （DDT）, which is one of the core problems in gas dynamic combustion.
基金Project supported by the National Natural Science Foundation of China （Grant No.10671120）
文摘In this paper, a simplest scalar nonconvex ZND combustion model with viscosity is considered. The existence of the global solution of the Riemann problem for the combustion model is obtained by using the fixed point theorem.
基金The project supported by the National Outstanding Youth Science Foundation of China the National Post Doctor Science Foundation of China
文摘In this paper, by means of combining non-probabilistic convex modeling with perturbation theory, an improvement is made on the first order approximate solution in convex models of uncertainties. Convex modeling is extended to largely uncertain and non-convex sets of uncertainties and the combinational convex modeling is developed. The presented method not only extends applications of convex modeling, but also improves its accuracy in uncertain problems and computational efficiency. The numerical example illustrates the efficiency of the proposed method.
文摘The sparse phase retrieval aims to recover the sparse signal from quadratic measurements. However, the measurements are often affected by outliers and asymmetric distribution noise. This paper introduces a novel method that combines the quantile regression and the L<sub>1/2</sub>-regularizer. It is a non-convex, non-smooth, non-Lipschitz optimization problem. We propose an efficient algorithm based on the Alternating Direction Methods of Multiplier (ADMM) to solve the corresponding optimization problem. Numerous numerical experiments show that this method can recover sparse signals with fewer measurements and is robust to dense bounded noise and Laplace noise.
基金the National Natural Science Foundation of China (Grant No.10471062)the Natural Science Foundation of Jiangsu Province (Grant No. BK2006184)
文摘The new trust region subproblem with the conic model was proposed in 2005, and was divided into three different cases. The first two cases can be converted into a quadratic model or a convex problem with quadratic constraints, while the third one is a nonconvex problem. In this paper, first we analyze the nonconvex problem, and reduce it to two convex problems. Then we discuss some dual properties of these problems and give an algorithm for solving them. At last, we present an algorithm for solving the new trust region subproblem with the conic model and report some numerical examples to illustrate the efficiency of the algorithm.
文摘针对传统水平集方法在分割灰度不均匀图像的过程中存在分割精度低的问题,提出一种自适应区域拟合的非均匀图像分割算法。首先构建自适应的区域拟合能量项来保留更多待分割图像局部区域内的细节信息,实现图像的准确分割;其次引入非凸正则项来平滑曲线并保护图像的边缘;然后添加能量惩罚项对水平集函数进行约束,提高算法的分割效率;最后对合成图像和真实图像进行实验验证。实验结果表明,所提算法的Dice相似系数平均值为88.62%,Jaccard相似系数平均值为79.86%,准确率平均值为92.48%,比Local Binary Fitting(LBF)、Local and Global Intensity Fitting(LGIF)、Local Pre-fitting(LPF)三种模型的总体平均值分别高18.19个百分点、16.10个百分点、13个百分点。
