约束优化

Conjugate gradient method is a method for solving nonlinear optimization problems, especially large-scale problems.

共轭梯度法是求解无约束优化问题的一种重要的方法，尤其适用于大规模优化问题的求解。

Solving constrained optimization problems of improved particle swarm optimization, we want to help.

详细说明：求解约束优化问题的改进粒子群优化算法，希望对大家有所帮助。

On the other hand, if the damage position and the damage size are used for description of the structural damage, the mathematical model is actually stated as a discrete structural optimization problem with unknown number of design variables, since the number of damages can not be given in advance.

本文采用极大极小问题构造损伤识别的优化模型，通过凝聚函数将极大极小问题转化为一个目标函数连续可微的无约束优化问题，采用基于灵敏度分析的序列线性规划方法求解。

In thesis, the generalized symmetric eigenvalue problem can be recasted into an unconstrained optimization problem.

本文先对广义特征分解问题进行建模，将瑞利商优化问题转化为无约束优化问题。

In this paper, we construct the differential equation to solve the unconstrained optimization problem. Such methods solving the ill-conditioned problems are very effective. It indicates that the asymptotically stable region of explicit the Euler method to solve the differential equation equals to the descent region of the gradient method to solve the original unconstrained optimization problem.

我们发现，在用Euler方法求解二次优化问题的等价动力系统的方程时，由方法的步长确定的稳定区域对应于这些方法所得到的迭代公式的步长满足单调下降算法的条件确定的单调下降区域，因此我们可以利用这个性质构造解无约束优化问题的数值方法而不采用标准的常微分方程的数值求解公式。

Based on this reformulation, we first give the conditions under which the stationary point of unconstrained optimization problem is a solution of GNCP, and then give the conditions under which Hessian matrix of vector-valued function is nonsingular.

基于此转化形式，我们首先研究优化问题的稳定点为GNCP问题解的充分条件，然后建立无约束优化问题的向量价值函数的Hessian矩阵非奇异的充分条件。

By using generalized projection matrix, conditions are given on the scalars in the three term-memory gradient direction to ensure that the three term-memory gradient projection direction is a descent direction. A new three term-memory gradient projection method for nonlinear programming with nonlinear equality and in-equality constraints is presented.

利用广义投影矩阵，对求解无约束规划的三项记忆梯度算法中的参数给一条件，确定它们的取值范围，以保证得到目标函数的三项记忆梯度广义投影下降方向，建立了求解非线性等式和不等式约束优化问题的三项记忆梯度广义投影算法，并证明了算法的收敛性。

In the third chapter, we concerned PVT algorithms for bound constrained optimization problem and proposed two feasible PVT algorithms.

第三章，我们对含边界约束的PVT算法进行了研究，给出了求解边界约束优化问题的PVT可行算法。

The experiment results on 13 well-known benchmark problems show that the proposed algorithm is capable of improving the search performance significantly in convergent speed and precision with respect to four techniques representative of the state-of-the-art in constrained optimization such as evolutionary algorithm based on homomorphous maps, artificial immune response constrained evolutionary strategy, constraint handling differential evolution, and evolutionary strategies based on stochastic ranking.

对13个标准测试问题的测试结果表明：与动态惩罚函数的进化算法、人工免疫响应约束进化策略、可行性规则的差分进化算法以及采用随机排序的进化策略相比，新算法在收敛速度和求解精度上均具有一定的优势。关键词：人工智能；差分进化算法；约束优化；随机排序

This paper proposes an Improved Particle Swarm Optimization algorithm.IPSO adopts a new mutation operator and a new method that congregates some neighboring individuals to form multiple sub-populations in order to lead particles to explore new search space.Additionally,this algorithm incorporates a mechanism with a simple and easy penalty function to handle constraint.Thus,this algorithm has strong global exploratory capability and efficiency while being applied to solve nonlinear constrained optimization problems.

提出了一种改进的粒子群算法（Improved Particle Swarm Optimization，IPSO），使用了一种新型的变异策略，并在搜索过程中将部分邻近的个体聚集成核，从而形成多子群引导粒子探测新的搜索区域，采用了简单易行的罚函数约束处理机制，使算法在求解较难的非线性约束优化问题时具有很强的全局搜索能力与效率。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。