全局收敛移动渐近线法子问题的求解与数值验证  

Solution and numerical verification of sub-problem of globally convergent version of MMA

作　　者：郭丽华[1] 汤文成[2] 齐文春[1] 黄莺[1] 

机构地区：[1]苏州科技学院机械工程学院,江苏苏州215009 [2]东南大学机械工程学院,江苏南京211189

出　　处：《机械设计》2014年第6期13-17,共5页Journal of Machine Design

基　　金：江苏省高校自然科学研究面上资助项目(11KJB460009);江苏省自然科学基金资助项目(BK2011314)

摘　　要：对全局收敛移动渐近线法构造的子问题进行了深入研究。基于子问题的凸性、可分性和保守性,应用Lagrange对偶方法求解子问题,给出了对偶问题的具体构造步骤。应用最优性条件将含不等式约束的原始非线性规划问题简化为只包含Lagrange乘子的非负约束优化问题。采用序列无约束极小化方法将对偶问题转变为无约束优化问题,并通过共轭梯度法求解。最后,通过桁架结构优化问题验证了算法的可行性,与其他算法相比可减少计算时间,提高收敛速度。The sub-problem of GCMMA（the Globally Conver- gent Version of Method of Moving Asymptotes）was deeply studied. Based on the convex,separable and conservative properties of sub- problem,a dual problem was built with Lagrange dual method. By using optimality conditions,the primal nonlinear programming problem with inequality constraints was simplified to a nonnegative constraints optimization only including Lagrange multiplier. The du- al problem was transformed into unconstrained optimization problem by using SUMT（Sequential Unconstrained Minimization Technique） and solved by conjugating gradient method. Finally, the feasibility of GCMMA is demonstrated by truss structural optimization prob- lem. Compare with other optimization algorithms, GCMMA needs less computing time and has higher convergence rate.

关 键 词：全局收敛移动渐近线法 LAGRANGE对偶 序列无约束极小化方法 桁架结构优化 

分 类 号：TH12[机械工程—机械设计及理论]