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	1. A Proximal Method for Solving Vector Variational Inequalities
	CHEN Chun-Rong
	Mathematics 25 September 2013
	Show/Hide Abstract \| Cite this paper︱Full-text: PDF (0 B)

	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. A new polynomial-time interior-point algorithms for the Cartesian $P_*(kappa)$-SCLCP
	WANG Guoqiang,BAI Yanqin
	Mathematics 20 February 2012
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	Abstract:In this paper, we generalize primal-dual interior-point method, which wasstudied by Bai et al. [Y.Q. Bai, M. El Ghami and C. Roos, ewblock {A new efficient large-update primal-dual interior-point method based on a finite barrier,} ewblock {SIAM J. Optim.} 13(3), 766-782 (2003)]for linear optimization to the Cartesian P*(k)-linear complementarity problem over symmetric conesvia Euclidean Jordan algebras. The symmetry of the resulting search directionsis forced by using the Nesterov-Todd scaling scheme.Moreover, we derive the iteration-bounds that match the currently bestknown iteration-bounds for large- and small-update methods, namelyO((1+2k)√￣r log r log r/ε) and O((1+2k)√￣r log r/ε), respectively,where r denotes the rank of the associated Euclidean Jordanalgebra and $arepsilon$ the desired accuracy.
	TO cite this article:WANG Guoqiang,BAI Yanqin. A new polynomial-time interior-point algorithms for the Cartesian $P_*(kappa)$-SCLCP[OL].[20 February 2012] http://en.paper.edu.cn/en_releasepaper/content/4465263


	3. Weak convergence theorem for variational inclusions and variational inequalities
	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, variational inequalities and fixed point problems in real Hilbert spaces. A modified extragradient algorithm for finding common solutions is proposed and analyzed. Three sequences generated by this algorithm are derived to converge weakly to a common solution by virtue of the Opial condition of Hilbert spaces, demiclosedness principle for nonexpansive mappings and the coincidence of solutions of variational inequalities with zeros of maximal monotone operators.
	TO cite this article:Zeng Liuchuan. Weak convergence theorem for variational inclusions and variational inequalities[OL].[ 6 January 2011] http://en.paper.edu.cn/en_releasepaper/content/4404738

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