Congying Han

Parallel Variable Distribution Algorithm for Constrained Optimization with Nonmonotone Technique

A modified parallel variable distribution (PVD) algorithm for solving large-scale constrained optimization problems is developed, which modifies quadratic subproblem at each iteration instead of the of the SQP-type PVD algorithm proposed by C. A. Sagastizabal and M. V. Solodov in 2002. The algorithm can circumvent the difficulties associated with the possible inconsistency of subproblem of the original SQP method. Moreover, we introduce a nonmonotone technique instead of the penalty function to carry out the line search procedure with more flexibly. Under appropriate conditions, the global convergence of the method is established. In the final part, parallel numerical experiments are implemented on CUDA based on GPU (Graphics Processing unit).

Parallel SSLE algorithm for large scale constrained optimization

In this paper, a parallel SSLE algorithm is proposed for solving large scale constrained optimization with block-separable structure. At each iteration, the PVD sub-problems are solved inexactly by the SSLE algorithm, which successfully overcomes the constraint inconsistency exited in most SQP-type algorithm, and decreases the computation amount as well. Without assuming the convexity of the constraints, the algorithm is proved to be globally convergent to a KKT point of the original problem.

On the convergence of asynchronous parallel algorithm for large-scale linearly constrained minimization problem

As a synchronization parallel framework, the parallel variable transformation (PVT) algorithm is effective to solve unconstrained optimization problems. In this paper, based on the idea that a constrained optimization problem is equivalent to a differentiable unconstrained optimization problem by introducing the Fischer Function, we propose an asynchronous PVT algorithm for solving large-scale linearly constrained convex minimization problems. This new algorithm can terminate when some processor satisfies terminal condition without waiting for other processors. Meanwhile, it can enhances practical efficiency for large-scale optimization problem. Global convergence of the new algorithm is established under suitable assumptions. And in particular, the linear rate of convergence does not depend on the number of processors.

Generalized Graph Regularized Non-negative Matrix Factorization for Data Representation

In this paper, a novel method called Generalized Graph Regularized Non-Negative Matrix Factorization (GGNMF) for data representation is proposed. GGNMF is a part-based data representation which incorporates generalized geometrically-based regularizer. New updating rules are adopted for this method, and the new method convergence is proved under some specific conditions. In our experiments, we evaluated the performance of GGNMF on image clustering problems. The results show that, with the guarantee of the convergence, the proposed updating rules can achieve even better performance.

Distributed Parallel Algorithm For Nonlinear OptimizationWithout Derivatives

This paper formulates a pattern search method for nonlinear programming. A distributed parallel algorithm is given based on the pattern search method by distributing the direction to every processor. Promising experimental results of the distributed parallel pattern method are obtained on a sixteen-machines cluster system by running the environment MPI.

Shrinking gradient descent algorithms for total variation regularized image denoising

Total variation regularization introduced by Rudin, Osher, and Fatemi (ROF) is widely used in image denoising problems for its capability to preserve repetitive textures and details of images. Many efforts have been devoted to obtain efficient gradient descent schemes for dual minimization of ROF model, such as Chambolle’s algorithm or gradient projection (GP) algorithm. In this paper, we propose a general gradient descent algorithm with a shrinking factor. Both Chambolle’s and GP algorithm can be regarded as the special cases of the proposed methods with special parameters. Global convergence analysis of the new algorithms with various step lengths and shrinking factors are present. Numerical results demonstrate their competitiveness in computational efficiency and reconstruction quality with some existing classic algorithms on a set of gray scale images.

A novel fingerprint classification method based on deep learning

Fingerprint classification is an effective technique for reducing the candidate numbers of fingerprints in the stage of matching in automatic fingerprint identification system (AFIS). In recent years, deep learning is an emerging technology which has achieved great success in many fields, such as image processing, computer vision. In this paper, we have a preliminary attempt on the traditional fingerprint classification problem based on the new depth neural network method. For the four-class problem, only choosing orientation field as the classification feature, we achieve 91.4% accuracy using the stacked sparse autoencoders (SAE) with three hidden layers in the NIST-DB4 database. And then two classification probabilities are used for fuzzy classification which can effectively enhance the accuracy of classification. By only adjusting the probability threshold, we get the accuracy of classification is 96.1% (setting threshold is 0.85), 97.2% (setting threshold is 0.90) and 98.0% (setting threshold is 0.95) with a single layer SAE. Applying the fuzzy method, we obtain higher accuracy.

Energy Losses and Voltage Stability Study in Distribution Network with Distributed Generation

With the distributed generation technology widely applied, some system problems such as overvoltages and undervoltages are gradually remarkable, which are caused by distributed generations like wind energy system (WES) and photovoltaic system (PVS) because of their probabilistic output power which relied on natural conditions. Since the impacts of WES and PVS are important in the distribution system voltage quality, we study these in this paper using new models with the probability density function of node voltage and the cumulative distribution function of total losses. We apply these models to solve the IEEE33 distribution system to be chosen in IEEE standard database. We compare our method with the Monte Carlo simulation method in three different cases, respectively. In the three cases, these results not only can provide the important reference information for the next stage optimization design, system reliability, and safety analysis but also can reduce amount of calculation.

An NMF-Based Method for the Fingerprint Orientation Field Estimation

Fingerprint orientation field estimation is an important processing step in a fingerprint identification system. Orientation field shows a fingerprint’s whole pattern and globally depicts the basic shape, structure and direction. Therefore, how to exactly estimate the orientation is important. Generally, the orientation images are computed by gradient-based approach, and then smoothed by other algorithms. In this paper we propose a new method, which is based on nonnegative matrix factorization (NMF) algorithm, to initialize the fingerprint orientation field instead of the gradient-based approach. Experiments on small blocks of fingerprints prove that the proposed algorithm is feasible. Experiments on fingerprint database show that the algorithm has a better performance than gradient-based approach does.

An Accelerated Proximal Gradient Algorithm for Singly Linearly Constrained Quadratic Programs with Box Constraints

Recently, the existed proximal gradient algorithms had been used to solve non-smooth convex optimization problems. As a special nonsmooth convex problem, the singly linearly constrained quadratic programs with box constraints appear in a wide range of applications. Hence, we propose an accelerated proximal gradient algorithm for singly linearly constrained quadratic programs with box constraints. At each iteration, the subproblem whose Hessian matrix is diagonal and positive definite is an easy model which can be solved efficiently via searching a root of a piecewise linear function. It is proved that the new algorithm can terminate at an ε-optimal solution within O(1/ε) iterations. Moreover, no line search is needed in this algorithm, and the global convergence can be proved under mild conditions. Numerical results are reported for solving quadratic programs arising from the training of support vector machines, which show that the new algorithm is efficient.