semidefinite 中文意思是什麼

In this thesis, we study some open problems and conjectures about the linear complementarity problem. it consists of the next three aspects : firstly, we study murthys " open problem whether the augmented matrix is a q0 - matrix for an arbitary square matrix a, provide an affirmable answer to this problem, obtain the augmented matrix of a sufficient matrix is a sufficient matrix and prove the graves algorithm can be used to solve linear complementarity problem with bisymmetry po - matrices ; secondly, we study murthys " conjecture about positive semidefinite matrices and provide some sufficient conditions such that a matrix is a positive semidefinite matrix, we also study pang ' s conjecture, obtain two conditions when r0 - matrices and q - matrices are equivelent and some properties about e0 q - matrices ; lastly, we give a counterexample to prove danao ' s conjecture that if a is a po - matrix, a e " a p1 * is false, point out some mistakes of murthys in [ 20 ], obtain when n = 2 or 3, a e " a p1 *, i. e. the condition of theorem 3. 2 of [ 25 ] that a p0 can be deleted and obtain a e " a is an almost e - matrix if a is a co - matrix or column sufficient matrix

本文分為三個部分，主要研究了線性互補問題的幾個相關的公開問題以及猜想： （ 1 ）研究了murthy等在[ 2 ]中提出的公開問題，即對任意的矩陣a ，其擴充矩陣是否為q _ 0 -矩陣，給出了肯定的回答，得到充分矩陣的擴充矩陣是充分矩陣，並討論了graves演算法，證明了若a是雙對稱的p _ 0 -矩陣時， lcp （ q ， a ）可由graves演算法給出； （ 2 ）研究了murthy等在[ 6 ]中提出關於半正定矩陣的猜想，給出了半正定矩陣的一些充分條件，並研究了pang ~ -猜想，得到了只r _ 0 -矩陣與q -矩陣的二個等價條件，以及e _ 0 q -矩陣的一些性質； （ 3 ）研究了danao在[ 25 ]中提出的danao猜想，即，若a為p _ 0 -矩陣，則，我們給出了反例證明了此猜想當n 4時不成立，指出了murthy等在[ 20 ]中的一些錯誤，得到n = 2 ， 3時，即[ 25 ]中定理3 . 2中a p _ 0的條件可以去掉。

Both theoretical proof and numerical experiments indicate that this algorithm is convergent and effective for solving large - scale semidefinite programming. in the following section, we work over the bisection problems

數值實驗與理論分析均表明該演算法適用於求解大規模問題，且具有良好的收斂性；其次，研究了電路二等分問題。

The second part of this paper is mainly concerned about an interesting matrix inequality presented in [ 5 ], which is then generalized in m ~ " under the entry - wise nonnegative ordering. we introduced the concept of sub - kronecker product, and establish an inequality which relates the schur complement of a and b for positive semidefinite matrices a and b. our results improve the related known results obtained by t. l. markham and r. l. smith in 1998 ( see [ 5 ] )

第二部分研究了文獻[ 5 ]中提出的一個有趣的矩陣不等式，並將此不等式在逆m -矩陣中推廣，然後引入次kronecker乘法的概念，提出並證明了一個更廣泛的不等式，改進了t . l . markham和r . l . smith在[ 5 ]中的有關結果。

In the first part, we shall prove several inequalities involving symmetric positive semidefinite, general m - matrices and inverse m - matrice which are generalization of the classical oppenheim ' s inequality for symmetric positive semidefinite matrices

第一個部分給出了半正定矩陣，一般的m -矩陣以及逆m -矩陣的一些相關不等式，而這些不等式都是有關半正定矩陣的經典的oppenheim不等式的推廣。

2. a new kind of algorithm, based on the golden section method for semidefinite programming is presented, which makes full use of the structure of the feasiable region

這種演算法是通過用黃金分割法在切割面上求優迭代求解的，具有簡便、計算量小的特點

As an application of succeeding, a numerical example of max - cut is given. 3. several semidefinite relaxation detection strategies of the cdma maximum likelihood multiuser detection are investigated. rounding, coordinate descent, cutting plane and branch and bound based on quadratic programming algorithm are presented to get the suboptirnal solution

本文紿出了基於半定規劃模型尋求多用戶檢測問題次優解的幾種重要方法，包括隨機擾動法、坐標下降法、半定規劃的割平面法和二次規劃的分枝定界法等

Lagrange duality and saddle points theorem for multiobjective semidefinite programming

對偶與鞍點定理

Then a is positive semidefinite, negative definite and negative semidefinite.

則A是半正定，負定，半負定的。

Then a is positive semidefinite, negative definite and negative semidefinite

則a是半正定，負定，半負定的。

A strength relaxation of semidefinite programming for standard quadratic optimization problems is given. the relaxation is transformed to a semi - indefinite programming. a linear programming cutting plane algorithm is proposed

3 .給出標準二次優化問題的一個強化半定規劃鬆弛模型，把該模型轉化為半不定的線性規劃問題，並提出線性規劃的一種新的割平面演算法解該問題，理論和數值實驗證明了演算法的有效性

Firstly, based on the s - subdifferential theory and strong duality of semidefinite programming, we propose one method to solve semidefinite programming

首先，本文提出一種求解半定規劃的占-次微分向量叢方法。

In this method, we get the optimal value of semidefinite programming by finding the optimal descent direction of its dual problem

該方法根據次微分理論與半定規劃的強對偶定理，通過求解對偶問題得到原始問題的最優值。

Minor self - conjugate and skewpositive semidefinite solutions to a system of matrix equations over skew fields

體上一矩陣方程組的次自共軛及斜亞半正定解

The semidefinite positive on the tensor product of matrix

矩陣張量積的半正定性

The eigenvalues of positive semidefinite matrices

半正定矩陣乘積的特徵值

Projection and contraction methods for semidefinite programming

解半定規劃的投影收縮法

Semidefinite programming is an extension of linear programming

半定規劃是線性規劃的一種推廣

A cut - plane algorithm for semidefinite programming and its application

半定規劃的割平面演算法及其應用

Positive semidefinite hermitian matrix solution of a matrix equations

特殊子空間上矩陣方程有解的判定

A new filter algorithm and its convergence of semidefinite programming

半定規劃問題的篩選演算法及其收斂性