可行方向法（简称为MFD）是用于求解非线性约束最优化重要的方法之一。
The method of feasible directions (MFD for short) is an important method for solving nonlin-early constrained optimization.
对于非线性约束最优化，提出了一个自动调节罚因子的信赖域类型的逐次线性算法。
This paper proposes a trust-region-type succesive linear algorithm with self-adjusted penalty parameter for nonlinear constrained optimization.
本文把最小外接球的评定问题表述为非线性约束最优化问题，并采用有效约束技术求得精确的最优解。
The equations of nonlinearly constrained optimization are presented for the evaluation of the minimal circumscribed sphere.
本文介绍把受约束非线性规划方法应用于热力设备最优化设计中进行初次试验的一些结果。
In this paper, some results of a trial applying the constrained nonlinear programming method in optimal design of thermal equipments are presented.
对非线性不等式约束最优化问题进行了讨论，借助广义投影建立求解问题的一个含系列自由参数的统一算法模型。
Optimization problem with nonlinear inequality constraints is discussed. With the help of the generalized projection, a unified algorithm model with a series of free parameters is presented.
把BFGS方法与混沌优化方法相结合，基于混沌变量提出一种求解具有变量边界约束非线性最优化问题的混合优化方法。
Combining the BFGS method with the chaos optimization method, a hybrid approach is proposed to solve nonlinear optimization problems with boundary restraints of variables.
本文给出非线性不等式约束最优化问题的一个初始点可任取的算法。
This paper presents an algorithm for nonlinear inequality constrained optimization problems which begins at any starting point.
对一般非线性等式约束最优化问题提出了一种信赖域算法，其子问题较易求解。
In this paper, a trust region algorithm for general nonlinear equality constrained optimization problems, is presented. The solution of their subproblems is easy.
对于一般的无约束最优化问题及其特殊情况非线性最小二乘问题而言，信赖域方法是一种有效的方法。
Trust region method is a kind of efficient methods to solve the general unconstrained optimization and its special situation, the nonlinear least squares problems.
经过推导，把一个四维带约束非线性最优化问题转化为一个二维无约束非线性最优化问题，并给出了求解过程。
After transforming the nonlinear optimal problem of four degrees of freedom with constraints to a nonlinear optimal problem of two degrees of freedom without constraints, the solution is given.
当考虑到发电机报价曲线的影响时，发电计划偏差优化问题是一个高维、离散、约束条件复杂的非线性最优化问题。
Considering the generators bidding prices curves, the generation scheduling error optimization problem is high dimensional, disperse, complex constrained, non-liner problem.
本文将非线性不等式约束下的非线性数学规划理论引入到水平井待钻井眼轨迹设计中，提出了水平井待钻井眼轨迹的最优化设计方法。
The paper introduces the nonlinear programming method under nonlinear constraints to well trajectory design while drilling and puts forward an optimization method for well trajectory design.
本文将非线性不等式约束下的非线性数学规划理论引入到水平井待钻井眼轨迹设计中，提出了水平井待钻井眼轨迹的最优化设计方法。
The paper introduces the nonlinear programming method under nonlinear constraints to well trajectory design while drilling and puts forward an optimization method for well trajectory design.
应用推荐