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Dive into the research topics where Guoping He is active.

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Featured researches published by Guoping He.


Applied Mathematics and Computation | 2009

A new smoothing Newton-type method for second-order cone programming problems

Liang Fang; Guoping He; Yunhong Hu

A new smoothing function of the well-known Fischer-Burmeister function is given. Based on this new function, a smoothing Newton-type method is proposed for solving second-order cone programming. At each iteration, the proposed algorithm solves only one system of linear equations and performs only one line search. This algorithm can start from an arbitrary point and it is Q-quadratically convergent under a mild assumption. Numerical results demonstrate the effectiveness of the algorithm.


Applied Mathematics and Computation | 2011

A smoothing Newton method for second-order cone optimization based on a new smoothing function

Jingyong Tang; Guoping He; Li Dong; Liang Fang

Abstract A new smoothing function is given in this paper by smoothing the symmetric perturbed Fischer–Burmeister function. Based on this new smoothing function, we present a smoothing Newton method for solving the second-order cone optimization (SOCO). The method solves only one linear system of equations and performs only one line search at each iteration. Without requiring strict complementarity assumption at the SOCO solution, the proposed algorithm is shown to be globally and locally quadratically convergent. Numerical results demonstrate that our algorithm is promising and comparable to interior-point methods.


Journal of Applied Mathematics | 2013

Parallel Variable Distribution Algorithm for Constrained Optimization with Nonmonotone Technique

Congying Han; Tingting Feng; Guoping He; Tiande Guo

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).


Computers & Mathematics With Applications | 2009

An active set quasi-Newton method with projected search for bound constrained minimization

Li Sun; Guoping He; Yongli Wang; Liang Fang

We analyze an active set quasi-Newton method for large scale bound constrained problems. Our approach combines the accurate active set identification function and the projected search. Both of these strategies permit fast change in the working set. The limited memory method is employed to update the inactive variables, while the active variables are updated by simple rules. A further division of the active set enables the global convergence of the new algorithm. Numerical tests demonstrate the efficiency and performance of the present strategy and its comparison with some existing active set strategies.


Applied Mathematics and Computation | 2009

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

Congying Han; Yongli Wang; Guoping He

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.


Science China-mathematics | 1997

An algorithm of sequential systems of linear equations for nonlinear optimization problems with arbitrary initial point

Ziyou Gao; Guoping He; Fang Wu

For current sequential quadratic programming (SQP) type algorithms, there exist two problems: (i) in order to obtain a search direction, one must solve one or more quadratic programming subproblems per iteration, and the computation amount of this algorithm is very large. So they are not suitable for the large-scale problems; (ii) the SQP algorithms require that the related quadratic programming subproblems be solvable per iteration, but it is difficult to be satisfied. By using ε-active set procedure with a special penalty function as the merit function, a new algorithm of sequential systems of linear equations for general nonlinear optimization problems with arbitrary initial point is presented. This new algorithm only needs to solve three systems of linear equations having the same coefficient matrix per iteration, and has global convergence and local superlinear convergence. To some extent, the new algorithm can overcome the shortcomings of the SQP algorithms mentioned above.


Optimization | 2014

An iteration primal–dual path-following method, based on wide neighbourhood and large update, for second-order cone programming

Zeng Zhe Feng; Liang Fang; Guoping He

In this article we propose a new primal-dual path-following interior point algorithm for second-order cone programming. Each iterate always follows the usual wide neighborhood , it does not necessarily stay within it, but must stay within the wider neighbourhood 𝒩(τ, β). We show that the algorithm has iteration complexity bound which is better than that of usual wide neighbourhood algorithm O(n log ϵ−1), where n is the dimension of the problem, with ϵ the required precision, α ∈ [0, 1] the given constant number and (x 0, s 0) the initial interior solution. It is the best result in regard to the iteration complexity bound in the context of path-following method for second-order cone programming.


Journal of Numerical Mathematics | 2013

A new non-interior continuation method for second-order cone programming

Jingyong Tang; Guoping He; Liang Fang

Abstract - We propose a new smoothing function in this paper by smoothing the symmetric perturbed Fischer-Burmeister function. Based on this new function, we present a new noninterior continuation method for solving the second-order cone programming. We adopt a variant merit function. Our algorithm needs to solve only one system of linear equations and to perform only one line search at each iteration. It can start from an arbitrary point and does not require the iteration points to be in the set of strictly feasible solutions. We prove the global and local quadratic convergence of the algorithm under suitable assumptions. Numerical results indicate that our algorithm performs well.


ieee international conference on progress in informatics and computing | 2010

Privacy-preserving SVM classification on arbitrarily partitioned data

Yunhong Hu; Guoping He; Liang Fang; Jingyong Tang

With the development of information science and modern technology, it becomes more important about how to protect privacy information. In this paper, a novel privacy-preserving support vector machine (SVM) classifier is put forward for arbitrarily partitioned data. The proposed SVM classifier, which is public but does not reveal the privately-held data, has accuracy comparable to that of an ordinary SVM classifier based on the original data. We prove the feasibility of our algorithms by using matrix factorization theory and show the security.


Applied Mathematics and Computation | 2004

Sequential systems of linear equations algorithm for nonlinear optimization problems--general constrained problems

Ziyou Gao; Guoping He; Fang Wu

In Ref. [J. Comput. Math. 20 (3) (2002) 301], a new superlinearly convergent algorithm of sequential systems of linear equations for nonlinear optimization problems with inequality constraints was proposed. Since the new algorithm only needs to solve four systems of linear equations having a same coefficient matrix per iteration, the computation amount of the algorithm is much less than that of the existing sequential quadratic programming algorithms per iteration. Under some mild assumptions, the new algorithm is globally convergent and its rate of convergence is one-step superlinearly. In this paper, it is shown that the new algorithm also can be used to deal with nonlinear optimization problems having nonlinearly equality and inequality constraints, by solving an auxiliary problem. Some numerical results are reported.

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Congying Han

Chinese Academy of Sciences

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Jingyong Tang

Shanghai Jiao Tong University

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Yongli Wang

Shandong University of Science and Technology

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Li Dong

Xinyang Normal University

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Liang Fang

Shanghai Jiao Tong University

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Li Sun

Shanghai Jiao Tong University

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Yunhong Hu

Shandong University of Science and Technology

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Jinchuan Zhou

Shandong University of Technology

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Tiande Guo

Chinese Academy of Sciences

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Changyin Zhou

Shandong University of Science and Technology

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