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Home > Papers > Optimization

There are 49 papers published in subject: > since this site started.

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	1. 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


	2. 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

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	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


	4. 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


	5. 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


	6. Generalized KKM Theorems on Hadamard Manifolds with Applications
	Zhou Liwen ,Huang Nanjing
	Mathematics 24 June 2009
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	Abstract:In this paper, a new notion of KKM mapping is introduced and a generalized KKM theorem is proved on Hadamard manifolds. As applications, an existence theorem of solution for a generalized mixed variational inequality and a fixed point theorem for a set-valued mapping are obtained on Hadamard manifolds.
	TO cite this article:Zhou Liwen ,Huang Nanjing . Generalized KKM Theorems on Hadamard Manifolds with Applications[OL].[24 June 2009] http://en.paper.edu.cn/en_releasepaper/content/33385


	7. A Combined Homotopy Method for Solving Horizontal Linear
	JUNYAN XU,ZHUANG MIAO,QINGHUAI LIU
	Mathematics 20 April 2009
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	Abstract:A global convergence combined homotopy method for solving horizontal linear complementarity problem has been introduced in this paper. We give the combined homotopy equation and prove in details the existence of the smooth path from almost any interior initial point to a solution of HLCP ( , , ). We give several preliminary numerical results. Numerical results are presented to show the effectiveness of this method.
	TO cite this article:JUNYAN XU,ZHUANG MIAO,QINGHUAI LIU. A Combined Homotopy Method for Solving Horizontal Linear[OL].[20 April 2009] http://en.paper.edu.cn/en_releasepaper/content/31550


	8. A New Online Algorithm for Multiclass of SVM
	zhang leilei,Sheng Baohuai
	Mathematics 25 March 2009
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	Abstract:In the present paper we provide a new algorithm for muticlass vector machines. Our starting point is a generalized notion of the maximal margin to multiclass problems. Using this notion we cast the muticlass problem as a binary classification task every time. So we combine a new classification function with the approximate maximal margin algorithm which is devised for binary classification.Our algorithm needs O( (p−1) α2γ2 ) corrections every time to separate the data with p-norm margin larger than l(1 − α)γ, with γ being the p-norm margin of the data.
	TO cite this article:zhang leilei,Sheng Baohuai. A New Online Algorithm for Multiclass of SVM[OL].[25 March 2009] http://en.paper.edu.cn/en_releasepaper/content/30712


	9. The Aggregate Constraint Shiffting Homotopy Method for Constrained Sequential Max-min Problem
	Wang Xiuyu,Jiang Xingwu,Liu Qinghuai
	Mathematics 11 February 2009
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	Abstract: For solving the constrained sequential max-min problem(CSMMP),the twice aggregate constraint shifting function with a parameter and a combined homotopy equation were construced, under the conditions of the feasible set bounded and connected .The convergence of a smooth homotopy path that from any interior point to a solution of the problem is prove. And we give two numerical examples, numerical examples show that this method is feasible and effective.
	TO cite this article:Wang Xiuyu,Jiang Xingwu,Liu Qinghuai. The Aggregate Constraint Shiffting Homotopy Method for Constrained Sequential Max-min Problem[OL].[11 February 2009] http://en.paper.edu.cn/en_releasepaper/content/28856


	10. Constraint Shifting Combined Homotopy Method for Solving D.C Programming
	Xu Junyan,Miao Zhuang,Tan Jiawei ,Liu Qinghuai
	Mathematics 11 February 2009
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	Abstract:A constraint shifting combined homotopy method for solving D.C programming has been introduced. We give the constraint shifting combined homotopy equation and prove in details the existence of the smooth path from a given point to a KKT point to the considered problem under some condition. Numerical results are presented to show the effectiveness of this method.
	TO cite this article:Xu Junyan,Miao Zhuang,Tan Jiawei , et al. Constraint Shifting Combined Homotopy Method for Solving D.C Programming[OL].[11 February 2009] http://en.paper.edu.cn/en_releasepaper/content/28805

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