查询词典 regularly convex function

An modified BFGS algorithm to solve the unconstrained optimization, whose Hessian matrix of the minimum point of the convex function is rank one defect, is presented in this paper.

本文对凸函数在极值点的Hessian矩阵是秩亏一的情况下，给出了一类求解无约束优化问题的修正BFGS算法。

An modified BFGS algorithm o solve the unconstrained optimization, whose Hessian matrix of the minimum point of the convex function is rank one defect, is presented in this paper.

本文对凸函数在极值点的Hessian矩阵是秩亏一的情况下，给出了一类求解无约束优化问题的修正BFGS算法。

We establish a Lagrange multiplier theorem for strict efficiency in convex settings and express strict points as saddle points of an appropriate Lagrangian function.

讨论凸多目标最优化问题的严有效解，建立了拉格朗日乘子定理，并把严有效解表示为一个适当的拉格朗日函数的鞍

In this paper, we start with a new formulation which is proposed based on the K-SVCR method. We then transform it as a complementarity problem and further a strongly convex unconstrained optimization problem by using the implicit Lagrangian function.

在本文中，我们首先在K-SVCR方法的基础上提出了新的模型，然后把新模型转化成一个互补问题，并利用Lagrangian隐函数进一步转化成一个强凸的无约束优化问题。

To reduce the conservatism in the estimation, the Schur complements of the matrixes are applied to transform the problem of selecting a suitable quadratic Lyapunov function into a simple convex optimization problem with linear matrix inequality constraints.

同时为了减少保守性，利用矩阵的Schur补性质，将如何选取该二次型Lyapunov函数的问题转化为标准的LMI凸优化问题。

Firstly, the generalization of Fan-Ha section theorem and a general vector variational inequality without convexity assumption and minimax theorem of vector-valued function are obtained. Then, the quasi-montone vector variational inequality problem is concerned. Cx-quasi-monotone operator is defined in topological vector space, inner point of a closed convex set K is introduced, the relation between inner point and relative algebraic interior point is given, an existence result for quasi-monotone vector variational inequality is obtained.

第三章主要研究了向量变分不等式和极小极大定理(来源：3282AB83C论文网www.abclunwen.com)，建立了广义的Fan-Ha截口定理、新的向量变分不等式与极小极大定理，并在拓扑向量空间中定义了C_x-拟单调算子，引入了闭凸集K的inner点，给出了inner点与相对代数内点的关系，利用innK_c代替K的拓扑内部，建立了新的拟单调向量变分不等式。

This invention relates to MIMO test method in a multi-user MIMO radio communication system including: estimating the channel matrixes of all users at the base station, computing an orthogonal projecting matrix M of the interference matrix of each user and transmitting M to each user periodically, receiving data sent by the base station at the user end and getting the orthogonal projecting matrix M from the received data, transforming the MIMO test of a desired user to the minimum value of a K-element secondary convex function, in which, K expresses the number of sending antennas and getting estimation of the test data by a ball test method.

一种多用户多输入多输出无线通信系统中的MIMO检测方法，包括步骤：在基站估计所有用户的信道矩阵；计算每个用户的干扰用户矩阵的正交投影矩阵M，并将每个用户的正交投影矩阵M定期发送给每个用户；在用户端接收基站发送的数据，并从接收的数据中得到正交投影矩阵M；利用正交投影矩阵M将期望用户的MIMO检测转化为K元二次凸函数的极小值，其中K表示对期望用户而言，发送天线的个数；利用球检测的方法，得到检测数据的估计。

The Legendre transformation generated by uis 〓where uis a convex-monotone function,〓 is the normal mapping of u.

引进函数u的Legendre变换〓（3）这里u为凸单调函数，〓为u确定的法映射。

Value iteration based on the vector set results in the piecewise linear convex form of the optimal value function, which can also be used to obtain the optimal policy.

在向量集上进行的值迭代可以得到最优值函数的分段线性凸函数表示形式，同样也可以得到对应的策略。

And the expression of its subdifferential is developed in the case that the effective domain of the optimal value function is a non-empty convex set.

最后利用方向导数和次微分导出了广义半无限极大极小规划的一个一阶最优性条件及其等价形式。

Molecular Distillation is a kind of high vacuum distillation method, which is suitable for the separation of high boiling, heat sensitivity and viscidity products.

分子蒸馏技术是一种在高真空条件下进行的连续蒸馏过程，适合于分离高沸点、热敏性及具有生物活性的混合物。

They are to the Noughties what yuppies were to the Eighties .

那在六十年代是时髦的，但在八十年代肯定是过时了