在数学规划的领域里定义了互逆规划--各自目标函数与约束条件位置相互交换的一对规划.接着指出,尽管互逆规划与对偶规划在表面上似乎类似,但是二者存在5点不同:(1)是否为同一个问题的不同;(2)存在"对偶间隙"与否的不同;(3)设...在数学规划的领域里定义了互逆规划--各自目标函数与约束条件位置相互交换的一对规划.接着指出,尽管互逆规划与对偶规划在表面上似乎类似,但是二者存在5点不同:(1)是否为同一个问题的不同;(2)存在"对偶间隙"与否的不同;(3)设计变量数目的不同;(4)是否单目标与多目标问题的不同;(5)问题合理与否的不同.然后,基于互逆规划的定义,用以审视结构拓扑优化模型,给出如下结果:(1)从这个角度洞悉,在结构优化中,确实有不合理的模型一直被沿用着;(2)找到了修正不合理模型使之合理化的方法;(3)对于给定体积下的柔顺度最小化(MCVC)模型,指出了其不合理的原因;(4)MCVC模型实际是互逆规划的m方,由此建立起其对应的s方,即给出了多个柔顺度约束的体积最小化(MVCC)模型;(5)给出了MVCC模型中的结构柔顺度约束的物理解释和算法,论证了ICM(independent continuous and mapping)方法以往关于全局化应力约束的概念和方法;(6)数值算例表明了MCVC与MVCC模型作为互逆规划的差异,且印证了MVCC模型的合理性.MCVC模型在不同体积约束及多工况下不同的权系数时,得到最优拓扑不同;但MVCC模型在多工况柔顺度约束下可得到唯一的最优拓扑.展开更多
动态规划对于解决多阶段决策问题有明显效果。由于各种多阶段决策问题,往往具有不同的特点,比如,阶段有限或无限,一定或不定,时间参数离散或连续,决策过程确定或随机等,因此动态规划有多种模型。本文针对阶段数有限的离散确定性过程问...动态规划对于解决多阶段决策问题有明显效果。由于各种多阶段决策问题,往往具有不同的特点,比如,阶段有限或无限,一定或不定,时间参数离散或连续,决策过程确定或随机等,因此动态规划有多种模型。本文针对阶段数有限的离散确定性过程问题进行讨论。探讨其相应的逆推算法主要的数学思维,并进一步将相关知识点与思政教育相结合,拓展了动态规划逆推算法的理论体系。Dynamic programming has obvious effects on solving multi-stage decision-making problems. Since various multi-stage decision-making problems often have different characteristics, such as limited or unlimited stages, certain or indeterminate, discrete or continuous time parameters, and definite or random decision-making processes, so there are many models for dynamic programming. This article discusses the discrete deterministic process with a limited number of stages, discusses the main mathematical thinking of the corresponding reverse calculation algorithm, further combines the relevant knowledge points with ideological and political education, and expands the theoretical system of the dynamic programming reverse calculation algorithm.展开更多
Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS met...Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991), a class of new restarting conjugate gradient methods is presented. Global convergences of the new method with two kinds of common line searches, are proved. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously dif ferentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.展开更多
This paper obtains sufficient optimality conditions for a nonlinear nondifferentiable multiobjective semi-infinite programming problem involving generalized(C,α,ρ,d)-convex functions.The authors formulate Mond-Weir-...This paper obtains sufficient optimality conditions for a nonlinear nondifferentiable multiobjective semi-infinite programming problem involving generalized(C,α,ρ,d)-convex functions.The authors formulate Mond-Weir-type dual model for the nonlinear nondifferentiable multiobjective semiinfinite programming problem and establish weak,strong and strict converse duality theorems relating the primal and the dual problems.展开更多
文摘在数学规划的领域里定义了互逆规划--各自目标函数与约束条件位置相互交换的一对规划.接着指出,尽管互逆规划与对偶规划在表面上似乎类似,但是二者存在5点不同:(1)是否为同一个问题的不同;(2)存在"对偶间隙"与否的不同;(3)设计变量数目的不同;(4)是否单目标与多目标问题的不同;(5)问题合理与否的不同.然后,基于互逆规划的定义,用以审视结构拓扑优化模型,给出如下结果:(1)从这个角度洞悉,在结构优化中,确实有不合理的模型一直被沿用着;(2)找到了修正不合理模型使之合理化的方法;(3)对于给定体积下的柔顺度最小化(MCVC)模型,指出了其不合理的原因;(4)MCVC模型实际是互逆规划的m方,由此建立起其对应的s方,即给出了多个柔顺度约束的体积最小化(MVCC)模型;(5)给出了MVCC模型中的结构柔顺度约束的物理解释和算法,论证了ICM(independent continuous and mapping)方法以往关于全局化应力约束的概念和方法;(6)数值算例表明了MCVC与MVCC模型作为互逆规划的差异,且印证了MVCC模型的合理性.MCVC模型在不同体积约束及多工况下不同的权系数时,得到最优拓扑不同;但MVCC模型在多工况柔顺度约束下可得到唯一的最优拓扑.
文摘动态规划对于解决多阶段决策问题有明显效果。由于各种多阶段决策问题,往往具有不同的特点,比如,阶段有限或无限,一定或不定,时间参数离散或连续,决策过程确定或随机等,因此动态规划有多种模型。本文针对阶段数有限的离散确定性过程问题进行讨论。探讨其相应的逆推算法主要的数学思维,并进一步将相关知识点与思政教育相结合,拓展了动态规划逆推算法的理论体系。Dynamic programming has obvious effects on solving multi-stage decision-making problems. Since various multi-stage decision-making problems often have different characteristics, such as limited or unlimited stages, certain or indeterminate, discrete or continuous time parameters, and definite or random decision-making processes, so there are many models for dynamic programming. This article discusses the discrete deterministic process with a limited number of stages, discusses the main mathematical thinking of the corresponding reverse calculation algorithm, further combines the relevant knowledge points with ideological and political education, and expands the theoretical system of the dynamic programming reverse calculation algorithm.
文摘Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991), a class of new restarting conjugate gradient methods is presented. Global convergences of the new method with two kinds of common line searches, are proved. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously dif ferentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.
文摘This paper obtains sufficient optimality conditions for a nonlinear nondifferentiable multiobjective semi-infinite programming problem involving generalized(C,α,ρ,d)-convex functions.The authors formulate Mond-Weir-type dual model for the nonlinear nondifferentiable multiobjective semiinfinite programming problem and establish weak,strong and strict converse duality theorems relating the primal and the dual problems.
