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	1. 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


	2. A Aggregate Constraint Shifting Combined Homotopy Method
	Wang Xiuyu,Jiang Xingwu,Liu Qinghuai
	Mathematics 16 January 2009
	Show/Hide Abstract \| Cite this paper︱Full-text: PDF (0 B)

	Abstract:For solving nonlinear nonconvex programming problem with one convex constraint.First, We use non-convex constraint structure aggregate function，and then we construct constraint shifting function and combined homotopy equation, under the conditions of the feasible set bounded connected and the regularity of boundary. Convergence of a smooth homotopy path that from any interior point or any infeasible interior point to a solution of the problem is prove. Numerical examples concluded that this method is feasible and effective
	TO cite this article:Wang Xiuyu,Jiang Xingwu,Liu Qinghuai. A Aggregate Constraint Shifting Combined Homotopy Method [OL].[16 January 2009] http://en.paper.edu.cn/en_releasepaper/content/28002


	3. First Passage Models for Denumerable Semi-Markov Decision Processes with Nonnegative Discounted Costs
	Yonghui Huang,Guo Xianping
	Mathematics 12 January 2009
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	Abstract:This paper considers a first passage model for discounted semi-Markov decision processes with denumerable states and nonnegative costs. The criterion to be optimized is the expected discounted cost incurred during a first passage time to a given target set. We first construct a semi-Markov decision process under a given semi-Markov decision kernel and a policy. Then, we prove that the value function satisfies the optimality equation and there exists an optimal (or $\\epsilon$-optimal) stationary policy under suitable conditions by using a minimum nonnegative solution approach, and further we give some properties of optimal policies.In addition, a value iteration algorithm for computing the value function and optimal policies is developed and an example is given. Finally, it is showed that our model is an extension of the first passage models for both discrete-time and continuous-time Markov decision processes.
	TO cite this article:Yonghui Huang,Guo Xianping. First Passage Models for Denumerable Semi-Markov Decision Processes with Nonnegative Discounted Costs[OL].[12 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27677


	4. An unify version of Cauchy-Schwarz and Wielandt inequalities
	Yan Zizong
	Mathematics 02 January 2007
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	Abstract:Let $A$ be an $n\\\\times n$ positive Hermitian matrix with $n$ eigenvalues satisfying $\\\\lambda_1\\\\geq\\\\lambda_2\\\\geq\\\\cdots\\\\geq\\\\lambda_n$ and $x$ and $y$ be $n\\\\times 1$ two vectors with the angle $\\\\psi$. This paper prove the the following inequality \\\\[(x^Ay)^2\\\\leq \\\\min\\\\limits_{i,j}\\\\begin{pmatrix} \\\\frac{\\\\lambda_i\\\\cos^2\\\\frac{\\\\psi}{2}-\\\\lambda_j\\\\sin^2\\\\frac{\\\\psi}{2}}{\\\\lambda_i\\\\cos^2\\\\frac{\\\\psi}{2}+ \\\\lambda_j\\\\sin^2\\\\frac{\\\\psi}{2}}\\\\end{pmatrix}^2(x^Ax)(y^*Ay).\\\\] It is an unify version of Cauchy-Schwarz and Wielandt inequalities.
	TO cite this article:Yan Zizong. An unify version of Cauchy-Schwarz and Wielandt inequalities[OL].[ 2 January 2007] http://en.paper.edu.cn/en_releasepaper/content/10556

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