优化问题

First,this problem is converted into the problem of H_2 opmization constrainedby H_∞performance and pole location,then an auxiliary perfomance function is introduced,andthe former problem can be converted into the optimal problem of minimization of the auxiliaryperformance function with constraints described by a matrix equation,at Jast this problem issolved by lagrange multipliers,and the static output feedback controllers are designed.

首先将文题转化为一个具有H＿∞性能和系统闭环极点位置约束的系统H＿2性能优化问题。进而通过引入一个辅助性能函数，将其转化成有一个矩阵方程约束的辅助性能函数的最小化优化问题，并给出这个问题静态输出反馈控制器的解。

An optimization method is proposed to solve steady-state optimization problems by linear approximation of the object function and the Linear Matrix Inequalities Problem and Eigenvalue Problem of Linear Matrix Inequalities theory.

提出了将稳态优化问题的目标函数进行线性逼近及用可行性问题求解算法和特征值问题求解算法进行求解的优化方法。

An optimization method is proposed to solved steady-state optimization problems by quadratic approximation of the object function and the Linear Matrix Inequalities Problem and Eigenvalue Problem of Linear Matrix Inequalities theory.

提出了将稳态优化问题的目标函数进行二次逼近及用可行性问题求解算法和特征值问题求解算法进行求解的优化方法。

In the actual programming, management and control problems, there are a great number of optimization problems with multistage that can be effectively solved by dynamic programming .

在客观现实的规划、管理和控制问题中，存在着大量的多阶段优化问题，动态规划是解决多阶段优化问题的重要工具。

The latter have been seeking for an appropriate algorithm for solving an optimization problem expressed in a form of error norm between estimates from a proper forward model of light propagation in tissue and the measurements. Mathematically, this posed an ill-conditioned inverse problem.

间接法的核心是寻找解优化问题的合适的算法，此优化问题表示为正向模型和测量值间的误差范数形式，在数学上这是一个病态的非线性逆问题。

On this basis, anoptimization algorithm library named OPTLIB is formed. The study of dynamic optimization theory is followed. To solve the problem of thecoupling of the static and the dynamic parameters of the flying vehicle design, some auxiliaryvariables are introduced to deal with them together. Then the calculus of variation is adoptedand augment form of Pontryagin's Maximum Principle is derived.

研究了飞行器设计中的典型动态优化问题——轨迹优化问题及算法，针对飞行器设计中的静态参数和动态参数互相耦合的问题，引入辅助变量将静态参数和动态参数统一处理，在此基础上用变分法推导了极大值原理的增广形式，证明了单独的静态或动态最优并不等于总体最优。

It is known that a production sequencing problem in mixed-model assembly line falls into NP-hard class of combinatorial optimization problem and thus a large-sized problem may be computationally intractable.

本文应用一种解大规模组合优化问题，特别是NP完全组合优化问题的有效近似算法——模拟退火算法，来求解混流生产线的投产排序问题，克服了上述缺点。

I present cluster schema for combinatorial problem with clustering, design a new crossover operator cluster crossover, study the survival probability of c-schema under c-crossover, apply it successfully to graph coloring, load balancing and maximum spanning tree problems: give measurements of diversity in GA, set up varying crossover probability algorithms to maintain diversity, obtain good results when apply it in avoiding premature convergence and multi-modal functions optimization; establish GAC to be suitable for non stationary function, it can explore the change of environment and find the best solution even for some"anomalous"function.

针对聚类组合优化问题提出了聚类模式，设计了一种新的交换操作：聚类交换并研究了聚类模式在聚类交换操作下的生存可能性，成功的将聚类交换思想和算子应用于图着色、负载平衡和最大生成树问题，佐证了类理论，表明类理论可以指导新的应用算法设计；给出了GA中多样性的度量标准和维护多样性的动态交换概率算法，用于避免过早收敛和多峰函数优化，取得了较好的结果；构造了维持种群多样性以适应动态环境的方法GAC，在某些现有方法无能为力的问题上，GAC能够探测到环境变化，找到当前最优解。

A proper k total colouring of a graph G is a colouring to its vertices and edges using k colours such that no two adjacent or incident elements of G may be assigned the same colour.

利用梯度投影与罚函数相结合的技巧，将带不等式和等式约束的优化问题化成一个无约束问题，提出了初始点可任意的求解不等式、等式约束优化问题的摄动梯度投影算法；参数δk取不同的数还可以得到一类梯度投影算法，从而得出了在搜索方向和步长不精确条件下的梯度投影法，保证了在实际应用中更容易实现；在较弱条件下，证明了该算法的全局收敛性。

Since nonlinear problems more accurately describes the phenomena of the nature,thus thispaper considers nonlinear optimization problems and two important classes of nonlinear evolu-tion equations,and neural networks for nonlinear optimization problems is stressfully studied.

由于非线性问题更准确地描述了客观现象，因此本文考虑了非线性优化问题和两类重要的非线性发展方程，突出地研究了非线性优化问题的神经网络。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。