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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. Distributed fuzzy adaptive iterative learning control with initial-state learning for consensus of multi-agent systems with uncertain communication topology structure
	WU Hui,LI Junmin
	Mathematics 26 April 2017
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	Abstract:Distributed consensus problem is addressed in this paper for linearly parameterized multi-agent systems with uncertain communication topology structure under initial-state learning condition. T-S fuzzy models are presented to describe the uncertain communication topology structure, and a distributed iterative learning control protocol is proposed without using any global information for the consensus problem. The AILC protocols are designed with distributed initial-learning and it is not essential to fix the initial value at the start of each iteration. It is proved that the proposed protocol ensures all the internal signals in the multi-agnt system are bounded and the follower agents track the leader exactly on [0,T]. Sufficient conditions of perfectly consensus for multi-agent systems are obtained by appropriately constructing Lyapunov function. The formation control problem is also studied by converting to the consensus problem. Finally, the simulation examples are given to verify the efficacy of the theoretical analysis.
	TO cite this article:WU Hui,LI Junmin. Distributed fuzzy adaptive iterative learning control with initial-state learning for consensus of multi-agent systems with uncertain communication topology structure[OL].[26 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4726586

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	3. Successive Rank-One Decomposition of Higher-Order Symmetric Complex Tensors
	ZHANG Zhanghui,BAI Minru
	Mathematics 12 April 2017
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	Abstract:In order to get the symmetric canonical decomposition of the higher-order symmetric complex tensors, this paper extends the successive decomposition method to the tensor case, and proposes a successive symmetric rank-one complex approximation method to decompose the higher-order symmetric complex tensors. It notes that the successive decomposition of real tensors may actually be different over the real field and the complex field. We further show that a symmetric canonical decomposition could be obtained when the method is applied to a unitary diagonalizable tensor. Numerical part analyzes the solving method of solving the sub-problem. Numerical results verify the efficiency of the proposed method.
	TO cite this article:ZHANG Zhanghui,BAI Minru. Successive Rank-One Decomposition of Higher-Order Symmetric Complex Tensors[OL].[12 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4724791


	4. 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


	5. 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


	6. 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


	7. Lagrange Type Optimality Conditions of Constrained Multi-Objective Optimization Problems
	YOU Man-Xue,LI Sheng-Jie
	Mathematics 10 May 2016
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	Abstract:This paper aims at investigating Lagrangian type optimality conditions in the context of constrained multi-objective optimization problems via Image Space Analysis. The equivalence between the existence of a regular (linear) separation in the Image Space and the existence of a saddle point for Lagrangian function is derived. Furthermore, we give some examples of regular separation functions, especially we use Gerstewitz function and augmented Lagrangian function to construct nonlinear separation functions.
	TO cite this article:YOU Man-Xue,LI Sheng-Jie. Lagrange Type Optimality Conditions of Constrained Multi-Objective Optimization Problems[OL].[10 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4687572


	8. On the existence of Pareto efficient Nash equilibria in discontinuous games
	LIU Zhi-Gang, Hou Ji-Cheng
	Mathematics 10 November 2015
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	Abstract:In this paper, we give a new existence theorem on Pareto efficient Nash equilibrium for discontinuous N-person noncooperative games in the framework of topological spaces without any linear structures. Moreover, we provide some examples where it is straightforward to verify our conditions and the previous conditions do not apply.
	TO cite this article:LIU Zhi-Gang, Hou Ji-Cheng. On the existence of Pareto efficient Nash equilibria in discontinuous games[OL].[10 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4660949


	9. 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


	10. 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

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