论文部分内容阅读
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-problems of the construction of global convergence moving asymptotic method are studied in detail. Based on the convexity, separability and conservation of subproblems, the Lagrange dual method is used to solve the subproblem, and the specific construction steps of the dual problem are given. Applying the optimality conditions, the original nonlinear programming problem with inequality constraints is reduced to a nonnegative constrained optimization problem with only Lagrange multipliers. The dual unconstrained minimization method is used to transform the duality problem into an unconstrained optimization problem and to solve it by conjugate gradient method. Finally, the feasibility of the algorithm is verified by the truss structure optimization problem, which can reduce the computation time and improve the convergence speed compared with other algorithms.