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	1. Research on a second-order cone reformulating problem of CDT problem
	QU Yanming
	Mathematics 12 March 2019
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	Abstract:In this paper, we study a class of CDT problem with two quadratic constraints, one of which is the unit ball constraint and the other is the ellipsoid constraint. Select the appropriate hyperplane through the optimal line segment, without dividing the feasible region. In the case of the second-order cone recombination technique and the SDP relaxation method, the necessary and sufficient conditions for the existence of the dual gap in the second-order cone reformulating problem of the CDT problem are obtained, and the theoretical proof is given which is paved to reduce or even eliminate the dual gap of the CDT problem.
	TO cite this article:QU Yanming. Research on a second-order cone reformulating problem of CDT problem[OL].[12 March 2019] http://en.paper.edu.cn/en_releasepaper/content/4747715


	2. The system of variational inequalities with hierarchical fixed point problem constraint
	ZENG Liu-Chuan
	Mathematics 20 June 2016
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	Abstract:In this paper, we introduce a general composite implicit schemefor finding a common solution of a system of variational inequalities (SVI) anda generalized mixed equilibrium problem with the constraint of the hierarchicalfixed point problem (HFPP) for a strictly pseudocontractive mapping in a realHilbert space. The strong convergence theorem for such an implicit scheme isestablished under some suitable assumptions. The result is the extension andimprovement of some corresponding ones in the literature.
	TO cite this article:ZENG Liu-Chuan. The system of variational inequalities with hierarchical fixed point problem constraint[OL].[20 June 2016] http://en.paper.edu.cn/en_releasepaper/content/4698655

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	3. Existence of strong solutions for generalized vector equilibrium problems in Banach spaces
	ZENG Liu-Chuan
	Mathematics 17 June 2016
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	Abstract:The purpose of this paper is to study the existence of strong solutions for the generalizedvector equilibrium problem (for short, GVEP) with a variable ordering relation in reflexive Banachspaces. The existence theorem of strong solutions of the GVEP for monotone multifunction isestablished by virtue of the KKM-Fan theorem. The result is the extension and improvement ofsome corresponding ones in the literature.
	TO cite this article:ZENG Liu-Chuan. Existence of strong solutions for generalized vector equilibrium problems in Banach spaces[OL].[17 June 2016] http://en.paper.edu.cn/en_releasepaper/content/4698299


	4. On Holder Continuity of Solutions to Parametric Vector Quasiequilibrium Problems
	CHEN Chun-Rong
	Mathematics 25 September 2013
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	Abstract:In this paper, Holder continuity of the unique solution to a parametric vector quasiequilibrium problem is studied by using nonlinear scalarization approach. The well-known Gerstewitz nonlinear scalarization function as an efficient tool plays key roles, especially, its globally Lipschitz property is fully employed. The result obtained is new in the literature, and the approach via nonlinear scalarization is different from the ones used in related works.
	TO cite this article:CHEN Chun-Rong. On Holder Continuity of Solutions to Parametric Vector Quasiequilibrium Problems[OL].[25 September 2013] http://en.paper.edu.cn/en_releasepaper/content/4561643


	5. 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


	6. Weak convergence theorem for variational inclusions and fixed point problems
	Zeng Liuchuan
	Mathematics 06 January 2011
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	Abstract:This paper is concerned with the problem of finding common solutions of variational inclusions and fixed point problems in real Hilbert spaces. A hybrid extragradient-like algorithm for finding common solutions is proposed and analyzed. Two sequences generated by this algorithm are derived to converge weakly to a common solution by virtue of the Opial condition of Hilbert spaces and demiclosedness princi-ple for nonexpansive mappings.?
	TO cite this article:Zeng Liuchuan. Weak convergence theorem for variational inclusions and fixed point problems[OL].[ 6 January 2011] http://en.paper.edu.cn/en_releasepaper/content/4404744


	7. The Improvement Algorithm of Binary Quadratic Programming
	Ai Wenbao,Zhang Xin,Xiang wen
	Mathematics 11 November 2010
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	Abstract:This paper considers the binary quadratic programming problem like (P). We establish the improvement approximation algorithm (henceforth denoted AZX) for this problem based on the Charikar and Wirth's algorithm and use the semi-definite relaxation programming and convexity of quadratic function return a solution whose ratio to the optimum is the same as theirs. We can also guarantee that our AZX algorithm returns a solution to the MAX-CUT problem in the requirement of the sum of all weights of edges are nonnegative. In the Computational test, the performance of our AZX algorithm is significantly stronger than Charikar and Wirth's algorithm and analogous to the Goemans and Williamson's algorithm.
	TO cite this article:Ai Wenbao,Zhang Xin,Xiang wen. The Improvement Algorithm of Binary Quadratic Programming[OL].[11 November 2010] http://en.paper.edu.cn/en_releasepaper/content/4391304


	8. An LQP-based descent method for structured monotone variational inequalities
	Li Min
	Mathematics 11 December 2009
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	Abstract:This paper proposes a descent method to solve a class of structured monotone variational inequalities. The descent directions are constructed from the iterates generated by a prediction-correction method (Computational Optimization and Applications 35 (2006), 19-46), which is based on the logarithmic-quadratic proximal method. In addition, the optimal step-sizes along these descent directions are identified to accelerate the convergence of the new method. Finally, some numerical results for solving traffic equilibrium problems are reported.
	TO cite this article:Li Min. An LQP-based descent method for structured monotone variational inequalities[OL].[11 December 2009] http://en.paper.edu.cn/en_releasepaper/content/37487


	9. Homotopy Method for Constrained Sequential Max-min Problem With a bounded feasible field
	Liu Qinghuai,Wang Xiuyu,Tan Jiawei
	Mathematics 11 February 2009
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	Abstract:For solving the constrained sequential max-min problem(CSMMP).We construced twice aggregate constraint shifting function with a parameter and a combined homotopy equation, under the conditions of the feasible set bounded connected and the regularity of boundary. We proved the convergence of a smooth homotopy path of the problem . Numerical examples showed that this method is feasible and effective.
	TO cite this article:Liu Qinghuai,Wang Xiuyu,Tan Jiawei. Homotopy Method for Constrained Sequential Max-min Problem With a bounded feasible field[OL].[11 February 2009] http://en.paper.edu.cn/en_releasepaper/content/28789


	10. A Constraint Shifting Combined Homotopy Method For Solving Nonlinear Nonconvex Programming
	Wang Xiuyu,Jiang Xingwu,Liu Qinghuai
	Mathematics 04 February 2009
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	Abstract:For solving nonlinear nonconvex programming problem,we construct constraint shifting functios with a parameter and a combined homotopy equation. We just need the feasible filed be bounded connected 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 proved.Numerical examples conclued that this method is feasible and effective.
	TO cite this article:Wang Xiuyu,Jiang Xingwu,Liu Qinghuai. A Constraint Shifting Combined Homotopy Method For Solving Nonlinear Nonconvex Programming[OL].[ 4 February 2009] http://en.paper.edu.cn/en_releasepaper/content/28389

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