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	1. A Steepest Descent Method on Lie Groups and its Application in Localization Problem
	QIN Han, YING Shi-Hui
	Mathematics 09 January 2014
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	Abstract:In this paper, through defining a universal steepest descent direction, an intrinsic iteration algorithm for optimization problem on Lie groups is proposed. Besides two global convergence theorems about the algorithm, the convergence analysis shows that the algorithm is at least linearly convergent. As an application example, the proposed algorithm is applied to the localization problem of workpiece machining. The numerical results show that the algorithm is really steepest descent and hence efficient.
	TO cite this article:QIN Han, YING Shi-Hui. A Steepest Descent Method on Lie Groups and its Application in Localization Problem[OL].[ 9 January 2014] http://en.paper.edu.cn/en_releasepaper/content/4581505


	2. Rainbow matchings and minimum color degree
	LI Hua-Long, WANG Guang-Hui, YAN Gui-Ying
	Mathematics 20 December 2013
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	Abstract:Let $G$ be an edge-colored graph. A rainbowmatching of $G$ is a matching in which no two edges have thesame color. Let $hat{delta}$ denote the minimum color degree of $G$, i.e. the smallest number of distinct colors on the edges incident with a vertex over all vertices. We show that if $\|V(G)\|geq 4hat{delta}-5$ when $hat{delta}geq 4$,then $G$ has a rainbow matching of size $hat{delta}$, which improves the previous result.
	TO cite this article:LI Hua-Long, WANG Guang-Hui, YAN Gui-Ying. Rainbow matchings and minimum color degree[OL].[20 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4576838

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	3. On the harmonic index of acyclic conjugated molecular graphs
	ZHU Yan, CHANG Ren-ying
	Mathematics 18 December 2013
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	Abstract:The harmonic index $H(G)$ of a graph $G$ is defined as the sum ofweights $rac{2}{d(u)+d(v)}$ of all edges $uv$ of $G$, where $d(u)$denotes the degree of a vertex $u$ in $G$. In this paper, we firstpresent a sharp lower bound on the harmonic index of acyclicconjugated molecular graphs (trees with a perfect matching). A sharplower bound on the harmonic index of acyclic graphs is also given interms of the order and given size of matching.
	TO cite this article:ZHU Yan, CHANG Ren-ying. On the harmonic index of acyclic conjugated molecular graphs[OL].[18 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4575821


	4. Remarks on Regularized Gap Functions and Error Bounds for Vector Variational Inequalities
	Li Lili,Chen Chunrong
	Mathematics 04 November 2013
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	Abstract:In this paper, modified versions of corresponding results on error bounds for (generalized) vector variational inequalities obtained by Sun and Chai (Optim. Lett., 2013) are given. Moreover, a framework to construct regularized gap functions for (generalized) vector variational inequalities is established. The main results obtained are new in the literature.
	TO cite this article:Li Lili,Chen Chunrong. Remarks on Regularized Gap Functions and Error Bounds for Vector Variational Inequalities[OL].[ 4 November 2013] http://en.paper.edu.cn/en_releasepaper/content/4567993


	5. A Novel Regularized Alternating Least Squares Algorithm with Global Convergence for Canonical Tensor Decomposition
	CHEN Yannan, SUN Wenyu
	Mathematics 29 October 2013
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	Abstract: The regularization method could deal with the swamp effect of alternating least squares (ALS) algorithms for tensor decomposition. The regularization term is a norm of the difference between the solution and the current iterate. In this paper, we show that the norm could be weakened to a seminorm so the selection of the regularization term could be more flexible. To overcome the swamp effect and avoid the drawback that the Hessian of the subproblem may get close to singular in the iterative procedure, we propose a seminorm regularized ALS algorithm for solving the canonical tensor decomposition. %In computation, the seminorm regularization term is added conveniently by replacing the Hessian %by its modified eigenvalue decomposition or the modified Cholesky factorization. Moreover, in new algorithm, we introduce a novel extrapolation in the update of each mode factor which makes an immediate impression on the update of subsequent ones. Under some mild assumptions, the global convergence of new algorithm with a seminorm regularization and the novel extrapolation is established. Numerical experiments on synthetic and real-world problems show that the new method is efficient and promising.
	TO cite this article:CHEN Yannan, SUN Wenyu. A Novel Regularized Alternating Least Squares Algorithm with Global Convergence for Canonical Tensor Decomposition[OL].[29 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4566786


	6. A Nonmonotone Adaptive Trust Region Method Based on Simple Conic Model for Unconstrained Optimization
	ZHAO Lijuan,SUN Wen-Yu
	Mathematics 29 October 2013
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	Abstract:In this paper, we propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region method, the subproblem in our method is a simple conic model, where the Hessian of the objective function is approximated by a scalar matrix. The trust region radius is adjusted with a new self-adaptive adjustment strategy which makes use of the information of the previous iteration and current iteration. The new method needs less memory and computational complexity. The global convergence and $Q$-superlinear convergence of the algorithm are established under the mild conditions. Numerical results on a series of standard test problems are reported to show that the new method is effective and attractive for large scale unconstrained optimization problems.
	TO cite this article:ZHAO Lijuan,SUN Wen-Yu. A Nonmonotone Adaptive Trust Region Method Based on Simple Conic Model for Unconstrained Optimization[OL].[29 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4566783


	7. Primal and dual objective space algorithms for solving linear multiplicative programmes
	SHAO Li-zhen,Ehrgott Matthias
	Mathematics 15 October 2013
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	Abstract:%It is known that for most of gene expression data for cancer classification, the number of samples is quite small compared to the number of genes. Therefore, feature selection is an essential pre-processing step and a challenging problem to remove the irrelevant or redundant genes before classification.Multiplicative programming (MPP) problems are global optimisation problems known to be NP-hard.In this paper, we focus on linear MPP problems. First, we improve our own objective space cut and bound algorithm for convex MPPs in the special case of linear MPPs by only solving one linear program at each iteration step instead of two as the previous version indicates. We call this algorithm ``primal objective space algorithm". Then based on the dual variant of Benson's algorithm, we propose a ``dual objective space algorithm" for solving linear MPP problems. Again the dual algorithm requires solving only one scalar linear program in each iteration step. We prove the correctness of the dual algorithm and use computational experiments to demonstrate the superiority of the new algorithms compared to existing algorithms from the literature.
	TO cite this article:SHAO Li-zhen,Ehrgott Matthias. Primal and dual objective space algorithms for solving linear multiplicative programmes[OL].[15 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4564266


	8. A LEGENDRE-GALERKIN SPECTRAL METHOD FOR FLOW OPTIMALCONTROL PROBLEM WITH $H^1$-NORM STATE CONSTRAINT
	CHEN Yan-Ping, HUANG Feng-Lin
	Mathematics 04 October 2013
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	Abstract:In this paper, we consider an optimal control problem with $H^1$-normsate constraint, governed by Stokes equations.The control problem is approximated by Legendre-Galerkin spectral method,which provides very accurate approximations with a relatively small number ofunknowns. Choosing appropriate basis functions leads to discrete systemswith sparse matrices. We first proposed the optimality conditions ofthe exact and the discrete optimal control systems, thenderive both a priori and a posteriori error estimates for controlproblem. Finally, an illustrative numerical experiment indicate that the proposed method is veryeffective for this kind of control problems.
	TO cite this article:CHEN Yan-Ping, HUANG Feng-Lin. A LEGENDRE-GALERKIN SPECTRAL METHOD FOR FLOW OPTIMALCONTROL PROBLEM WITH $H^1$-NORM STATE CONSTRAINT[OL].[ 4 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4561453


	9. A Nonmonotonic Self-Adaptive Trust Region Algorithm Without Line Search
	Hang Dan,Zhou Qunyan
	Mathematics 01 October 2013
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	Abstract:In this paper,we propose a nonmonotone trust region method for unconstrained optimization.Our method can be regarded as a combination of nonmonotone technique ,fixed steplength and self-adaptive trust region,when a trial step is not accepted ,the method doesn't resolve the subproblem but generates a iterative point whose steplength is defined by formula. Under mild conditions,we prove that the algorithm is global convergence and superlinear convergence. Numerical results are also presented.
	TO cite this article:Hang Dan,Zhou Qunyan. A Nonmonotonic Self-Adaptive Trust Region Algorithm Without Line Search[OL].[ 1 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4562233


	10. 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

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