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	1. The optimization conditions for generalized complementarity problems based on generalized Fisher-Burmeister functions
	Wei-Zhe Gu,Mohamed A.Tawhid
	Mathematics 17 June 2016
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	Abstract:In this article, we consider an unconstrained minimization reformulation of the generalized complementarity problem GCP(f, g) based on the generalized Fisher-Burmeister function. Starting with the continuously differentiable functions f and g, we show under certain conditions any stationary point of the unconstrained minimization problem is a solution to GCP .
	TO cite this article:Wei-Zhe Gu,Mohamed A.Tawhid. The optimization conditions for generalized complementarity problems based on generalized Fisher-Burmeister functions[OL].[17 June 2016] http://en.paper.edu.cn/en_releasepaper/content/4697419


	2. Convergence Analysis on a Derivative-Free Descent Method for Nonlinear Complementarity Problems
	Wei-Zhe Gu,Li-Yong Lu
	Mathematics 17 June 2016
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	Abstract:Recently, Hu, Huang and Chen, in the paper[Properties of a family of generalized NCP-functions and a derivative free algorithm for complementarity problems] introduced a family of generalized NCP-functions, which include many existing NCP-functions as special cases. They obtained several favorite properties of the functions; and by which, they showed that a derivative-free descent method is globally convergent under suitable assumptions. However, no result on convergent rate of the method was reported. In this paper, we further investigate some properties of this family of generalized NCP-functions. In particular, we show that, under suitable assumptions, the iterative sequence generated by the descent method discussed in their paper converges globally at a linear rate to a solution of the nonlinear complementarity problem.
	TO cite this article:Wei-Zhe Gu,Li-Yong Lu. Convergence Analysis on a Derivative-Free Descent Method for Nonlinear Complementarity Problems[OL].[17 June 2016] http://en.paper.edu.cn/en_releasepaper/content/4697495

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	3. A Novel Regularized Alternating Least Squares Algorithm with Global Convergence for Canonical Tensor Decomposition
	CHEN Yannan, SUN Wenyu
	Mathematics 29 October 2013
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	Abstract: The regularization method could deal with the swamp effect of alternating least squares (ALS) algorithms for tensor decomposition. The regularization term is a norm of the difference between the solution and the current iterate. In this paper, we show that the norm could be weakened to a seminorm so the selection of the regularization term could be more flexible. To overcome the swamp effect and avoid the drawback that the Hessian of the subproblem may get close to singular in the iterative procedure, we propose a seminorm regularized ALS algorithm for solving the canonical tensor decomposition. %In computation, the seminorm regularization term is added conveniently by replacing the Hessian %by its modified eigenvalue decomposition or the modified Cholesky factorization. Moreover, in new algorithm, we introduce a novel extrapolation in the update of each mode factor which makes an immediate impression on the update of subsequent ones. Under some mild assumptions, the global convergence of new algorithm with a seminorm regularization and the novel extrapolation is established. Numerical experiments on synthetic and real-world problems show that the new method is efficient and promising.
	TO cite this article:CHEN Yannan, SUN Wenyu. A Novel Regularized Alternating Least Squares Algorithm with Global Convergence for Canonical Tensor Decomposition[OL].[29 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4566786


	4. A Nonmonotone Adaptive Trust Region Method Based on Simple Conic Model for Unconstrained Optimization
	ZHAO Lijuan,SUN Wen-Yu
	Mathematics 29 October 2013
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	Abstract:In this paper, we propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region method, the subproblem in our method is a simple conic model, where the Hessian of the objective function is approximated by a scalar matrix. The trust region radius is adjusted with a new self-adaptive adjustment strategy which makes use of the information of the previous iteration and current iteration. The new method needs less memory and computational complexity. The global convergence and $Q$-superlinear convergence of the algorithm are established under the mild conditions. Numerical results on a series of standard test problems are reported to show that the new method is effective and attractive for large scale unconstrained optimization problems.
	TO cite this article:ZHAO Lijuan,SUN Wen-Yu. A Nonmonotone Adaptive Trust Region Method Based on Simple Conic Model for Unconstrained Optimization[OL].[29 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4566783


	5. A Hybrid Spectral Conjugate Gradient Method with Self-adjusting Property
	Cui Dandan,Xue Wei,Yu Gaohang
	Mathematics 18 January 2012
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	Abstract: In this paper, we present a hybrid spectral conjugate gradient method with self-adjusting property which producesdescent search direction at every iteration. Its global convergence can be established with the standard Wolfe conditions. Numerical results indicate that the proposed method is efficient and promising.
	TO cite this article:Cui Dandan,Xue Wei,Yu Gaohang. A Hybrid Spectral Conjugate Gradient Method with Self-adjusting Property[OL].[18 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4463023


	6. Multivariate spectral gradient projection method for large-scale nonlinear systems ofmonotone equations
	YU Gaohang,NIU Shanzhou
	Mathematics 11 January 2012
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	Abstract: In this paper, we propose a multivariate spectral gradient method for solving la- rge-scalenonlinear systems of monotone equations. Under some suitable conditions, we showthat the method is globally convergent. Some favorable properties of the proposed methodin- clude the following cases: (1) the global convergence is independent of any merit function;(2) it can be applied to solving nonsmooth equations;(3) the global convergence theorem is esta- blished without Lipschitz continuity anddifferentiability on the equation. The preliminary n- umerical results show that the proposedmethod is practically effective.
	TO cite this article:YU Gaohang,NIU Shanzhou. Multivariate spectral gradient projection method for large-scale nonlinear systems ofmonotone equations[OL].[11 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4460684


	7. Stochastic Multiobjective Problems with Equilibrium Constraints
	Lin Guihua
	Mathematics 09 February 2011
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	Abstract:In this paper, we consider stochastic multiobjective problems with equilibrium constraints. Several Pareto stationarities concepts are presented. We reformulate the Pareto stationarity conditions to mixed complementarity problems. Asymptotic methods and applications are described for the SMOPCC.
	TO cite this article:Lin Guihua. Stochastic Multiobjective Problems with Equilibrium Constraints[OL].[ 9 February 2011] http://en.paper.edu.cn/en_releasepaper/content/4410399


	8. Inexact Alternating Direction Based Contraction Methods for Separable Linearly Constrained Convex Programming
	Guoyong Gu,Bingsheng He, Junfeng Yang,Junfeng Yang
	Mathematics 27 January 2010
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	Abstract:Alternating direction method (ADM) has been well studied in the context of linearly constrained convex programming problems. In the last few years, we have witnessed a number of novel applications arising from image processing, compressive sensing and statistics, etc., where the ADM approach is surprisingly efficient. In common applications of the ADM, both the objective function and the constraints are separable into two parts. Recently, the ADM has been extended to the case where the number of separable parts is a finite number. However, in each iteration, the subproblems are required to be solved exactly. In this paper, by using some reasonable inexactness criteria, we propose two inexact alternating direction based contraction methods, which substantially broaden the applicable scope of the ADM.
	TO cite this article:Guoyong Gu,Bingsheng He, Junfeng Yang,Junfeng Yang. Inexact Alternating Direction Based Contraction Methods for Separable Linearly Constrained Convex Programming[OL].[27 January 2010] http://en.paper.edu.cn/en_releasepaper/content/39530


	9. Combined Homotopy Method For Solving Nonconvex
	Liu Qinghuai,Wang Xiuyu,Jiang Xingwu
	Mathematics 05 February 2009
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	Abstract:For solving nonlinear nonconvex programming problem with a bounded feasible set. An aggregate constraint shifting function with a parameter and a combined homotopy equation are proposed, under the conditions of the feasible set bounded 、connectedand and the regularity of boundary. .The convergence of a smooth homotopy path that from any interior point or any infeasible interior point to a solution of the problem is prove. Numerical examples conclued that this method is feasible and effective.
	TO cite this article:Liu Qinghuai,Wang Xiuyu,Jiang Xingwu. Combined Homotopy Method For Solving Nonconvex [OL].[ 5 February 2009] http://en.paper.edu.cn/en_releasepaper/content/28428


	10. A Aggregate Constraint Shifting Combined Homotopy Method for Solving Nonlinear Programming
	Wang Xiuyu,Jiang Xingwu,Liu qinghuai
	Mathematics 05 February 2009
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	Abstract:For solving nonlinear nonconvex programming problem only with inequality constraint, We construct aggregate constraint shifting function with a parameter , and combined homotopy equation, under very weak conditions of the feasible set bounded、 connected and the regularity of the boundary.The convergence of a smooth homotopy path which from any interior point or any infeasible interior point to a solution of the problem is proved. Numerical examples concluded that this method is feasible and effective.
	TO cite this article:Wang Xiuyu,Jiang Xingwu,Liu qinghuai. A Aggregate Constraint Shifting Combined Homotopy Method for Solving Nonlinear Programming[OL].[ 5 February 2009] http://en.paper.edu.cn/en_releasepaper/content/28421

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