变几何域传热的表面热流反演方法

变几何域的表面热流反演是一类特殊的热传导逆问题,在再入飞行器烧蚀型防热材料的表面热流反演中具有工程实用价值.本文首先对变几何域传热的正问题计算方法进行了校核验证,然后建立了求解变几何域表面热流反演问题的顺序函数法和共轭梯度法;给出了这两种反演方法的基本思想和算法推导,并针对典型算例进行了仿真.结果表明:两种反演方法都能计算出较好的反演结果,并且算法受测量噪声的影响较小,具有较好的鲁棒性;反演算法能适应不同的几何域变化函数,但几何域变化量的测量误差在表面热流的反演结果中会有较为直接的反映.     

基于改进粒子群算法的翼型多目标优化研究

在多目标优化研究中,为改善多目标粒子群算法的局部搜索能力,以标准粒子群算法为基础,引入单点模拟退火算法,局部进化最优个体,采用基于目标向量的共享函数法评价适应值.标准测试函数优化实例表明:本文算法比标准粒子群算法具有更好的收敛稳定性和收敛速度,收敛速度提高了近50%;针对某翼型的气动优化设计结果表明:改进算法有效缩短了优化时间,迭代代数由61减为49,调用CFD由4880减为4250次;阻力系数、升力系数、低头力矩系数分别改进了9.23%、0.42%、16.4%,取得了较好的优化效果.     

桁架结构截面优化设计的改进模拟退火算法

将模拟退火算法应用于桁架结构截面尺寸优化设计,提出若干方法改进了算法的鲁棒性、计算效率和求解精度。通过一批经典问题,同时与传统结构优化算法和遗传算法进行了比较。数值结果表明,本文的改进模拟退火算法具有很高的优化求解精度,计算效率有显著提高且优于遗传算法,有望在结构优化设计问题中发挥其特点。     

Exactness of penalization for exact minimax penalty function method in nonconvex programming

The exact minimax penalty function method is used to solve a noncon-vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con-strained optimization problem are invex with respect to the same function η (with the exception of those equality constraints for which the associated Lagrange multipliers are negative-these functions should be assumed to be incave with respect to η). Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf-ficient to prove the results.     

基于广义可靠性的随机模糊杆系结构优化设计

研究了随机参数杆系结构的广义可靠性优化设计问题。导出了随机荷载作用下以模糊许用值为条件的结构广义可靠度计算公式;建立了以杆截面为设计变量、结构重量均值为目标函数、结构模糊位移和单元模糊强度广义可靠度为约束条件的优化数学模型;通过引入罚函数,将原广义可靠性约束优化问题转化为无约束优化问题,利用遗传算法求解。设计结果表明:文中提出的模型和计算公式是可行有效的。     

求解线性方程组的一种新方法

将线性方程组的一般系数矩阵转化为对称正定矩阵,从而把原线性方程组的求解问题转化为一个等价变分问题的极少值点寻优问题,借助对分寻优法进行求解。算例结果表明,本文方法不仅对于良态线性方程组的求解问题是有效的,而且对于病态线性方程组的求解问题同样是有效的。     

Auxiliary principle and approximation solvability for system of new generalized mixed equilibrium problems in reflexive Banach spaces

A new system of generalized mixed equilibrium problems (SGMEPs) involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalized mixed equilibrium problems (SAGMEPs) for solving the SGMEPs is first introduced. Existence and uniqueness of the solutions to the SAGMEPs is proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces. Using the auxiliary principle technique, a new iterative algorithm for solving the SGMEPs is proposed and analyzed. Strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild assumptions without any coercive conditions. These results improve, unify, and generalize some recent results in this field.     

Auxiliary principle and approximation solvability for system of new generalized mixed equilibrium problems in reflexive Banach spaces

A new system of generalized mixed equilibrium problems (SGMEPs) involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalized mixed equilibrium problems (SAGMEPs) for solving the SGMEPs is first introduced. Existence and uniqueness of the solutions to the SAGMEPs is proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces. Using the auxiliary principle technique, a new iterative algorithm for solving the SGMEPs is proposed and analyzed. Strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild assumptions without any coercive conditions. These results improve, unify, and generalize some recent results in this field.     

Parallel Multisplitting AOR method for solving a class of system of nonlinear algebraic equations

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Iterative algorithm for solutions to new system of generalized mixed implicit equilibrium

A new system of generalized mixed implicit equilibrium problems(SGMIEP) involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces.First,an auxiliary mixed equilibrium problem(AMEP) is introduced.The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions.Next,by using the solution mapping of the AMEP,a system of generalized equation problems(SGEP) is considered,and its equivalence with the SGMIEP is shown.By using the SGEP,a new iterative algorithm for solving the SGMIEP is proposed and analyzed.The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions.These results are new,which unify and generalize some recent results in this field.     

Computer computation of the method of multiple scales—dirichlet problem for a class of system of nonlinear differential equations

The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations. The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales. Contributed by Jiang Fu-ru, Original Member of Editorial Committe, AMM Biography: Xie La-bing (1976∼); Jiang Fu-ru(1927∼)