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	1. A Proximal Method for Solving Vector Variational Inequalities
	CHEN Chun-Rong
	Mathematics 25 September 2013
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	Abstract:In this paper, based on choosing at each iteration a different vectorization to the iterated matrix, a proximal-type method for solving the weak vector variational inequality problem (mbox{WVVI}) in finite-dimensional spaces is proposed. Under appropriate assumptions, it was proved that the generated subsequence converges to a solution of problem $(mbox{WVVI})$, if the problem $(mbox{WVVI})$ has strong solutions. Moreover, if the solution set of $(mbox{WVVI})$ coincides with its strong solution set, then the whole sequence converges to a strong solution of problem (mbox{WVVI}).
	TO cite this article:CHEN Chun-Rong. A Proximal Method for Solving Vector Variational Inequalities[OL].[25 September 2013] http://en.paper.edu.cn/en_releasepaper/content/4561636


	2. An Aggregate Function Method for Constrained Optimization Problems
	ZHANG Xinchun
	Mathematics 30 June 2013
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	Abstract:In this paper, the aggregate function method (AFM) for constrained optimization problems (COP) is investigated. The AFM is effective for multiple inequality-constrained optimization problems. However, the inherent shortcomings of the AFM, both in convergence and data overflow, seem to have gone unnoticed. To address these issues systematically, some efficient measurements are carried out to deal with such problems, such as adding the stable term and the exponent reduction parameter to the original aggregate function, which are highlighted in the entire paper. Moreover, the corresponding properties of both the AFM and the improved AFM (IAFM) are presented.
	TO cite this article:ZHANG Xinchun. An Aggregate Function Method for Constrained Optimization Problems[J].

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	3. On the Wiener Index of Trees with Maximum Degree
	LI Jing,WEI Fuyi
	Mathematics 01 June 2013
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	Abstract:The Wiener index of a graph is the sum of distances between all unordered pairs of vertices of the graph. In this paper, the fourth and fifth smallest Wiener indices of all trees with maximum degree are determined. Moreover, partial extreme graphs which reach the above lower bounds are also given.
	TO cite this article:LI Jing,WEI Fuyi. On the Wiener Index of Trees with Maximum Degree[OL].[ 1 June 2013] http://en.paper.edu.cn/en_releasepaper/content/4546426


	4. Necessary optimality conditions for optimal control problems with set-valued constraints
	Li An
	Mathematics 08 April 2013
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	Abstract:In this paper, we consider optimal control problems with set-valued state and control constraints.The present constraints subsume the existing mixed equality and inequality constraints.The necessary optimality conditions for weak local minimum are derived for these problemsunder calmness and constraint qualification condition on the set-valued constraints,but without any convexity or differentiability assumptions on the original data.The novelty of this paper concerns both the nature of calmness andthe analytic techniques used to derive the results.
	TO cite this article:Li An. Necessary optimality conditions for optimal control problems with set-valued constraints[OL].[ 8 April 2013] http://en.paper.edu.cn/en_releasepaper/content/4535133


	5. The Utility of A Class of Economic Network
	Xu Lan,Xu Ying
	Mathematics 20 January 2013
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	Abstract:Networks play an important role in a wide range of economic phenomena. Despite this fact, standard economic theory rarely considers economic networks explicitly in its analysis. However, a major innovation in economic theory has been the use of methods stemming from graph theory to describe and study relations between economic agents in networks. This recent development has lead to a fast increase in theoretical research on economic networks. In this paper, we consider the utility of a class of economic network.
	TO cite this article:Xu Lan,Xu Ying. The Utility of A Class of Economic Network[OL].[20 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4514564


	6. An accelerated first-order gradient algorithm for singly linearly constrained quadratic programs with box constraints
	Li Mingqiang,Han Congying ,Wang Yongli,He Guoping
	Mathematics 20 January 2013
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	Abstract:In this paper, 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 $arepsilon-$optimal solution within $O(1/sqrt arepsilon)$ iterations. Moreover, no line search is needed in this new algorithm and the global convergence can be proved under mild conditions. Numerical results arereported for solving quadratic programs arising from the training of support vector machines, which show that the new algorithm is efficient.
	TO cite this article:Li Mingqiang,Han Congying ,Wang Yongli, et al. An accelerated first-order gradient algorithm for singly linearly constrained quadratic programs with box constraints[OL].[20 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4516737


	7. Three Types of Topological Indices of the Join of k Graphs
	LI Jing,WEI Fuyi
	Mathematics 19 January 2013
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	Abstract:The join of two vertex disjoint graphs is obtained from their union by including all edges between the vertices in one graph and the vertices in the other. This paper mainly focused on the calculation formulas of Wiener indices, hyper-Wiener indices and reverse Wiener indices of the join of k graphs based on two definitions.
	TO cite this article:LI Jing,WEI Fuyi. Three Types of Topological Indices of the Join of k Graphs[OL].[19 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4516584


	8. The Existence of Optimal Control for Fully Coupled Forward-Backward Stochastic Differential Equation System with Non-Lipschitz Cost Functional
	MENG Qingxin,ZHANG Qi
	Mathematics 18 December 2012
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	Abstract:In this paper, we study the existence of stochastic optimal control by a new application of the existence theorem of convex optimality. The stochastic system in our concern is a linear fully coupled forward-backward stochastic differential equation with a non-Lipschitz cost functional. Some typical examples, such as LQ problem, can be included in this studied stochastic system.
	TO cite this article:MENG Qingxin,ZHANG Qi. The Existence of Optimal Control for Fully Coupled Forward-Backward Stochastic Differential Equation System with Non-Lipschitz Cost Functional[OL].[18 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4504577


	9. A Method for 4-Color Evaluation of Plain Graph
	Yu Qiu
	Mathematics 25 June 2012
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	Abstract:In this paper introduced the method of minimum immovable edges for the calculation of color function. And according to the decompose method of similarity and difference, it introduced the principle that the color number reverse never happens. Through the analysis and calculation with this method and principle, it calculated the color number of 5-cycle configuration in graph T. And then introduced an equivalent definition that the coefficient a in part A is bigger than zero, which will be the same as the reducibility of n-cycle configuration in the graph T. Finally carried out the proof that the coefficient a in part A is bigger than zero for 5-cycle configuration in graph T.
	TO cite this article:Yu Qiu. A Method for 4-Color Evaluation of Plain Graph[OL].[25 June 2012] http://en.paper.edu.cn/en_releasepaper/content/4483107


	10. A line search filter-SQP method for nonlinear inequality constrained optimization
	YUAN Jing,ZHU Detong
	Mathematics 19 June 2012
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	Abstract:Filter methods are extensively studied for solving nonlinearprogramming problems (NLP). In this paper, the author propose the sequencequadratic programming method with a line search filter technique fornonlinear inequality constrained problems. The search direction ofthis algorithm is generated by first-order necessary conditions,while a backtracking line search procedure is used to generate stepsize. The second order correction is employed to overcome theMaratos effect. Local convergent rate and global convergence areestablished under some suitable conditions. Finally, the results ofnumerical experiments indicate that the proposed method is efficientfor the given test problems.
	TO cite this article:YUAN Jing,ZHU Detong. A line search filter-SQP method for nonlinear inequality constrained optimization[OL].[19 June 2012] http://en.paper.edu.cn/en_releasepaper/content/4482733

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