分类: 数学 >> 控制和优化 提交时间: 2016-12-16
摘要: Although the Karush-Kuhn-Tucker conditions suggest a connection between a conic optimization problem and a complementarity problem, it is difficult to find an accessible explicit form of this relationship in the literature. This note will present such a relationship.
分类: 数学 >> 数学(综合) 提交时间: 2016-11-09
摘要: In this paper, the $m-$order infinite dimensional Hilbert tensor (hypermatrix) is intrduced to define an $(m-1)$-homogeneous operator on the spaces of analytic functions, which is called Hilbert tensor operator. The boundedness of Hilbert tensor operator is presented on Bergman spaces $A^p$ ($p>2(m-1)$). On the base of the boundedness, two positively homogeneous operators are introduced to the spaces of analytic functions, and hence the upper bounds of norm of such two operators are found on Bergman spaces $A^p$ ($p>2(m-1)$). In particular, the norms of such two operators on Bergman spaces $A^{4(m-1)}$ are smaller than or equal to $\pi$ and $\pi^\frac1{m-1}$, respectively.
分类: 数学 >> 控制和优化 提交时间: 2016-08-30
摘要: In this paper necessary conditions and sufficient conditions are given for a linear operator to be a positive operators of an Extended Lorentz cone. Similarities and differences with the positive operators of Lorentz cones are investigated.
分类: 数学 >> 控制和优化 分类: 数学 >> 计算数学 提交时间: 2016-07-11
摘要: In this paper, we construct and analyze an efficient m-step Levenberg-Marquardt method for nonlinear equations. The main advantage of this method is that the m-step LM method could save more Jacobian calculations with frozen $(J_k^TJ_k+\lambda_kI)^{-1}J_k^T$ at every iteration. Under the local error bound condition which is weaker than nonsingularity, the m-step LM method has been proved to have $(m+1)$th convergence order. The global convergence has also been given by trust region technique. Numerical results show that the m-step LM method is efficient and could save many calculations of the Jacobian especially for large scale problems.
分类: 数学 >> 应用数学 提交时间: 2016-07-07
摘要: 自博弈论中有趣的海盗分金问题(Pirate Game(PG))提出以来,其在理论分析上,仅摘要:自博弈论中有趣的海盗分金问题(Pirate Game(PG))提出以来,其在理论分析上,仅限于逆向递推法和数列递推法。本文首先借鉴这两种方法建立一阶差分模型;而后,考虑到每个海盗不是绝对理性的,等级高的海盗需要依赖等级低一级的海盗的决策而做出最优决策,建立二阶时滞差分模型,在数学原理上对 PG 做深入分析:当τ= 0 时,与实际情况偏差较大;当时滞量 τ=1 时,模型的解和一阶差分模型的解一致,即在现实生活中也存在着做决策时直接咨询自己的第一副手的社会群体。从而,在现代分析方法的层次上,本文给出一个 PG 的新的合理的数学解释。
分类: 数学 >> 数学(综合) 提交时间: 2016-07-05
摘要: In this paper, the Pazy's Fixed Point Theorems of monotone $\alpha-$nonexpansive mapping $T$ are proved in a uniformly convex Banach space $E$ with the partial order ``$\leq$". That is, we obtain that the fixed point set of $T$ with respect to the partial order ``$\leq$" is nonempty whenever the Picard iteration $\{T^nx_0\}$ is bounded for some comparable initial point $x_0$ and its image $Tx_0$. When restricting the demain of $T$ to the cone $P$, a monotone $\alpha-$nonexpansive mapping $T$ has at least a fixed point if and only if the Picard iteration $\{T^n0\}$ is bounbed. Furthermore, with the help of the properties of the normal cone $P$, the weakly and strongly convergent theorems of the Picard iteration $\{T^nx_0\}$ are showed for finding a fixed point of $T$ with respect to the partial order ``$\leq$" in uniformly convex ordered Banach space.
分类: 数学 >> 代数与数论 提交时间: 2016-05-19
摘要: For CM elliptic curve over rational field with analytic rank one, for any potential good ordinary prime p, not dividing the number of roots of unity in the complex multiplication field, we show the p-part of its Shafarevich-Tate group has order predicted by the Birch and Swinnerton-Dyer conjecture.