A Lagrange multiplier method for semilinear elliptic state constrained optimal control problems

In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the original problem as well as weak convergence of the adjoint states and weak-* convergence of the multipliers associated to the state constraint. Moreover, we show existence of stationary points in arbitrary small neighborhoods of local solutions of the original problem. Additionally, various numerical results are presented.

Incomplete angle reconstruction algorithm with the sparse optimization and the image optimal criterions

To solve the problem of artifact and image degradation caused by incomplete angle projection, this article presents an incomplete angle reconstruction algorithm based on sparse optimization and image optimization criterion (SO-IOC). Firstly, the joint objective function model is established based on the projection sparsity and the natural features of images. Secondly, by means of the idea of alternating direction method of multipliers, the augmented Lagrange method is used to decompose the reconstruction model into simple subproblems and the modified genetic algorithm is used for solving those subproblems. Finally, a multiobjective optimization operation is carried out to coordinate and select the candidate solutions to improve the quality of the reconstructed images. The algebraic reconstruction technique algorithm and the Split Bregman algorithm are compared with the SO-IOC algorithm. In the compared process, the mean relative error and the peak signal-to-noise ratio are used. The experimental results show the SO-IOC algorithm is best among the above three algorithms.

Robust Mesh Denoising via Triple Sparsity

Mesh denoising is to recover high quality meshes from noisy inputs scanned from the real world. It is a crucial step in geometry processing, computer vision, computer-aided design, etc. Yet, state-of-the-art denoising methods still fall short of handling meshes containing both sharp features and fine details. Besides, some of the methods usually introduce undesired staircase effects in smoothly curved regions. These issues become more severe when a mesh is corrupted by various kinds of noise, including Gaussian, impulsive, and mixed Gaussian–impulsive noise. In this paper, we present a novel optimization method for robustly denoising the mesh. The proposed method is based on a triple sparsity prior: a double sparse prior on first order and second order variations of the face normal field and a sparse prior on the residual face normal field. Numerically, we develop an efficient algorithm based on variable-splitting and augmented Lagrange method to solve the problem. The proposed method can not only effectively recover various features (including sharp features, fine details, smoothly curved regions, etc), but also be robust against different kinds of noise. We testify effectiveness of the proposed method on synthetic meshes and a broad variety of scanned data produced by the laser scanner, Kinect v1, Kinect v2, and Kinect-fusion. Intensive numerical experiments show that our method outperforms all of the compared select-of-the-art methods qualitatively and quantitatively.

Study on Coupling Fault Dynamics of Sliding Bearing-Rotor System

The phenomenon of oil film oscillation and frequency locked may occur in a healthy rotor system which is supported by sliding bearing. The dynamic behavior of the rotor system with misalignment and rubbing coupling fault supported by sliding bearing is also very complex. To solve the problem of fault diagnosis in this case, a dynamical model of rotor system is proposed in this paper. The short bearing oil film force, the equivalent misalignment moment, and Hertz contact theory are applied to establish the model. For rubbing faults, the Augmented Lagrange method is used to deal with the contact constraints to ensure that the boundary penetration depth is within the specified tolerance range. Furthermore, the dynamic behavior of the faulty rotor system under different rubbing stiffness conditions is analyzed in this paper. Meanwhile, the fault signal is divided into equal-band by the wavelet basis functions to find out the fault frequency band of the rotor system. Finally, the accuracy of the simulation study is verified by measurements obtained from the faulty rotor test platform. The following findings are made in this paper. The rubbing fault is dominant in the coupling fault. With the increasing of the speed, the frequency components of the system are dominated by high frequency. The double frequency is the main fault feature frequency band. It can be seen that the rotor system moves gradually from a quasi-periodic state into chaos due to the Lyapunov exponent. At the same time, due to the effects of misalignment moment and friction force, the phenomenon of oil film instability is partially suppressed. The lagging of the first and second-order oil film oscillations occurs.

Augmented Lagrange Based on Modified Covariance Matching Criterion Method for DOA Estimation in Compressed Sensing

A novel direction of arrival (DOA) estimation method in compressed sensing (CS) is presented, in which DOA estimation is considered as the joint sparse recovery from multiple measurement vectors (MMV). The proposed method is obtained by minimizing the modified-based covariance matching criterion, which is acquired by adding penalties according to the regularization method. This minimization problem is shown to be a semidefinite program (SDP) and transformed into a constrained quadratic programming problem for reducing computational complexity which can be solved by the augmented Lagrange method. The proposed method can significantly improve the performance especially in the scenarios with low signal to noise ratio (SNR), small number of snapshots, and closely spaced correlated sources. In addition, the Cramér-Rao bound (CRB) of the proposed method is developed and the performance guarantee is given according to a version of the restricted isometry property (RIP). The effectiveness and satisfactory performance of the proposed method are illustrated by simulation results.

Small Infrared Target Detection Based on Low-Rank and Sparse Matrix Decomposition

Sparse and low-rank matrix decomposition (SLMD) tries to decompose a matrix into a low-rank matrix and a sparse matrix, it has recently attached much research interest and has good applications in many fields. An infrared image with small target usually has slowly transitional background, it can be seen as the sum of low-rank background component and sparse target component. So by SLMD, the sparse target component can be separated from the infrared image and then be used for small infrared target detection (SITD). The augmented Lagrange method, which is currently the most efficient algorithm used for solving SLMD, was applied in this paper for SITD, some parameters were analyzed and adjusted for SITD. Experimental results show our algorithm is fast and reliable.