The problem of monitoring the wear - line of a blast furnace is treated as the inverse problem of the static heat conduction system , and the latter has been turned into the optimization of the squared residual of the measured and calculated temperature at the sensor locations 摘要把确定高炉炉缸炉底热侵蚀边界归结为稳态热传导方程的反问题，并转化为极小化在若干测温点处由设定侵蚀边界对应的偏微分方程边值问题求得的温度与实测温度之间误差的优化问题。
Firstly , unlike the factorization - based methods that minimize the svd ( singular value decomposition ) re - projection error , the method uses the minimization of mean 2d re - projection error of projective points as a criterion , therefore it has a clearer physical meaning and enhances the accuracy of projective reconstruction results 该方法以全局性极小化射影三维空间点的二维反投影误差平方和为准则，相对于缩小svd反投影误差的方法，具有更为明确合理的物理意义。
Some heuristics for the problems are present , and their performance guarantee is analyzed by the transform lemma . some present results are improved . in part three , the problem of scheduling n jobs on a single ' batching machine is addressed , and the jobs have release times and due dates 第三部分研究了单台批处理机器，工件的到达时间不同，以极小化最大延迟时间为目标的分批排序问题1 | r _ j , b | lmax ，论文提出了一些近似算法，给出该了问题相应的最差性能比界。
In view of ill - posed characteristic of the equation , with variational principle , solving of a nonlinear hyperbolic equation is attributed to minimization of a functional . so the equation has unique solution through regularization theory . then variables of the functional are discretized and linearized with finite difference and nonlinear least squares techniques , accordingly minimization of the functional is converted into standard least square question 考虑到该方程具有病态特性，求得的解不唯一，具有一般数学物理反问题的特征，利用变分原理，将其转化为一个泛函的极小化问题，通过正则化处理，使原问题具有唯一解；然后应用有限差分思想和求解非线性最小二乘问题的方法，将泛函中的变量离散化和线性化，进而转化为一个标准最小二乘问题来求解。
Otherwise , the trust region radius is reduced and a new trial point is selected . it is possible that the region subproblem need to be resolved many times before obtaining an acceptable step , and hence the total computation for completing one iteration might be expensive . this article combines approximate trust region path and nonmonotonic backtracking strategy to solve nonlinear optimization subject to linear inequality constraints , that is , we use approximate trust region path to get the research direction by minimuming quadratical model in the trust region by employing 本文在求解线性不等式约束优化问题时，将近似信赖域路径与非单调信赖域方法相结合，即在信赖域半径内沿近似信赖域路径得到一极小化二次模型的搜索方向后采用回代法避免重复求解信赖域子问题，在此算法中当搜索方向不被接受时，就用非单调线搜索技术得到接受步长，定义新的迭代点。
The objectives are to minimize a linear function of total completion time and total variation of completion time , a linear function of total waiting time and total variation of waiting time , a cost function based on earliness , tardiness , window size , window location , and a linear function of the due date , the earliness and tardiness for all jobs 目标函数分别为极小化完工时间和与完工时间偏差和的线性组合，极小化等待时问和与等待时间偏差和的线性组合，极小化提前时间、延误时间、最早交货期及窗口长度的加权和，极小化提前时间、延误时间及公共工期的加权和。
Chapter 4 studies the techniques for numerical realization of the dual algorithms and generalization of the dual algorithms to general unconstrained nonlinear programming . at first , we construct modified dual algorithms to overcome the drawback that it needs to resolve a sequential unconstrained minimization problems exactly in the step 2 of the dual algorithms in chapter 2 and chapter 3 首先针对前两章的对偶算法由于需要精确求解一系列无约束极小化问题，因而实际计算中很难实现这一缺点，构造修正的对偶算法，即，关于势函数的无约束极小化问题无需精确求解的对偶算法。
Secondly , to counter contour curve for large sole of rubber overshoes , the way of linear circle arc spline of two dimensions curve fitting has been raised in this paper and autocad has meanwhile been applied in cad / cam integeration system of rubber overshoes mould , and also a whole set of software and hardware technique developed , and the selecting way for optimizing tool path worked out . this way may make nc machining free running minimun 其次，针对胶鞋大底的轮廓曲线，对圆弧样条进行了深入研究，提出了二维曲线拟合的线性化圆弧样条方法；同时将autocad应用于胶鞋模具cad / cam一体化系统中，成功地开发了一整套相应的软硬件应用技术，提出了刀具轨迹优化的动态选择法，以便使nc加工的空行程相对极小化。
Then , minimizing the performance by spectral factorization , we obtain an optimal controller design method , which can be used to take simultaneous account of model uncertainty and control energy constraint and evaluate optimal tracking performance and control energy in practical control system designs 然后通过谱分解极小化该性能指标，导出一个最优的控制器设计方法，可以兼顾模型不确定性和控制能量约束，在实际控制系统设计中可用来对最优跟踪性能和控制能量进行预估。
