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1. chinaXiv:201707.00007 [pdf]

B tensors and tensor complementarity problems

Yisheng Song; Wei Mei
分类: 数学 >> 控制和优化

In this paper, one of our main purposes is to prove the boundedness of solution set of tensor complementarity problem with B tensor such that the specific bounds only depend on the structural properties of tensor. To achieve this purpose, firstly, we present that each B tensor is strictly semi-positive and each B$_0$ tensor is semi-positive. Subsequencely, the strictly lower and upper bounds of different operator norms are given for two positively homogeneous operators defined by B tensor. Finally, with the help of the upper bounds of different operator norms, we show the strcitly lower bound of solution set of tensor complementarity problem with B tensor. Furthermore, the upper bounds of spectral radius and $E$-spectral radius of B (B$_0$) tensor are obtained, respectively, which achieves our another objective. In particular, such the upper bounds only depend on the principal diagonal entries of tensors.

提交时间: 2017-07-25 点击量1584下载量940 评论 0

2. chinaXiv:201608.00201 [pdf]

Conic optimization and complementarity problems V2

S. Z. N´emeth; Guohan Zhang
分类: 数学 >> 控制和优化

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.

提交时间: 2016-12-16 点击量1276下载量450 评论 0

3. chinaXiv:201608.00202 [pdf]

Positive operators of Extended Lorentz cones

S. Z. N´emeth; Guohan Zhang
分类: 数学 >> 控制和优化

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.

提交时间: 2016-08-30 点击量1298下载量682 评论 0

4. chinaXiv:201607.00035 [pdf]

An efficient m-step Levenberg-Marquardt method for nonlinear equations

Chen, Liang; Ma, Yanfang; Su, Chencheng
分类: 数学 >> 控制和优化

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.

提交时间: 2016-07-11 点击量1484下载量501 评论 0

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