无约束的

The Hestenes-Powell augmented Lagrangian function has been used for solving inequality constrained optimization problems via unconstrained minimization techniques.

增广拉格朗日函数法是用无约束极小化技术求解约束优化问题的一类重要方法。

In this paper, the Hestenes-Powell augmented Lagrangian function is again considered, for solving equality constrained problems via unconstrained minimization techniques.

本文对用无约束极小化方法求解等式约束非线性规划问题的Hestenes-Powell增广拉格朗日函数作了进一步研究。

In this paper, we succeed to generalize the modified BFGS update formula to constrained optimization problem.

本文将无约束问题的修正BFGS信赖域算法成功地应用于约束优化问题。

These experimental results demonstrate that CUA adapts to both constrained and unconstrained problems, and has the virtues of occupying little memory, computing quickly and accurately, supplies the designers with sufficient convenience during the design stage.

这些例子验证了CUA既可以求解约束问题，也可以求解无约束问题，并且具有占用内存小、计算速度较快和精度较高的优点，可以为设计者在产品设计阶段提供便利。

Based on the ICMmethod,the discrete topological optimization problem about spot-weld's existence or not is transformed into the continuous optimization problem on[0,1].The optimization model is founded with maximizing the structural stiffness as objective and structural strength as constraints.The problem of multi-objectives and multi-constraints is transformed into the problem of single-objective and single-constraint with the K-S function.The displacement and stress are transformed into the explicit function of design variables with the Response Surface Methodology.The optimization model is solved with Sequential Quadratic Program.

基于ICM（Independent Continuous Mapping，即独立、连续、映射）方法，将焊点有无的离散拓扑优化问题转化为[0，1]区间上的连续优化问题；建立了以结构刚度最大为目标、结构强度为约束的连续拓扑优化模型；采用K-S函数将多目标和多约束问题转化为单目标和单约束问题；运用响应面方法将位移和应力转化为设计变量的显式函数，采用序列二次规划方法求解优化模型。

In chapter 2 we propose a linear equality constraint optimization question , the new algorithm is combined with the new conjugate gradient method(HS-DY conjugate gradient method)and Rosen"s gradient projection method , and has proven it"s convergence under the Wolfe line search.In chapter 3 we have combined a descent algorithm of constraint question with Rosen"s gradient projection, and proposed a linear equality constraint optimization question"s new algorithm, and proposed a combining algorithm about this algorithm, then we have proven their convergence under the Wolfe line search, and has performed the numerical experimentation.

在第三章中我们将无约束问题的一类下降算法与Rosen投影梯度法相结合，将其推广到线性等式约束最优化问题，提出了线性等式约束最优化问题的一类投影下降算法，并提出了基于这类算法的混合算法，在Wolfe线搜索下证明了这两类算法的收敛性，并通过数值试验验证了算法的有效性。

An unconstrained cost function is provided for the Orthogonal Space-Time Block Coded Multi-input-Multi-Output Antenna System. The global minima of the cost function are analyzed: in fact the global minima of the cost function is the normalized channel vector.

该方法主要利用了正交特性，给出了一个针对正交空时分组码MIMO系统模型的无约束代价函数，并分析了该函数的全局最小值：该无约束代价函数的最小值实际上就是实际信道的归一化矢量。

The modified particle swarm optimization is utilized to solve the proposed reactive power optimization model; and combining with non–stationary multi-stage assignment penalty function, the reactive power optimization problem is transferred into a problem to solve extreme-value without constraints, thus the calculation accuracy and global convergence ability of MPSO are effectively improved, and power grid company can achieve maximal economic benefit by means of the proposed algorithm.

应用改进粒子群优化算法求解该无功优化模型，并结合动态调整罚函数法将无功优化问题转化成无约束求极值问题，从而有效地提高了改进粒子群优化算法的全局收敛能力和计算精度，使电网公司取得了最大经济效益。

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。

For boxing constraint of control, trigonometric function transformation was developed to achieve an unconstrained problem.

对于控制变量受箱型约束的问题，采用三角函数转换将其转化为控制无约束问题。

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。