【作者】 顾朗；

【导师】 陈中文；

【作者基本信息】 苏州大学 ， 应用数学， 2004， 硕士

【摘要】 传统的约束优化问题都需用到惩罚参数,理论上罚参数足够大一定保证收敛,但实际上往往会出现上溢而计算失败。1996年Fletcher等人首先提出过滤方法的设想,立即引起许多学者的关注,近几年已出现了一些成果。无惩罚型方法是一类新型的算法,M.Ulbrich等人就线性独立约束规格条件成立的情形作了研究,本文以此为依据,提出一个不需要线性独立约束规格条件成立的更一般的算法。我们对非线性等式约束优化问题的一类无惩罚型方法,在没有约束梯度线性独立的假设条件下,分析了在迭代点的可行性条件和效益函数同时改善的性质,讨论算法的全局收敛性,并进行数值试验。数值结果表明该种方法比较有效。更多还原

【Abstract】 For constrained optimization problem, common methods use penalty parameters. Theoretically, penalty parameters big enough ensure the convergence of the algorithm. However, they often lead to overflow so that the computation fails. Fletcher(1996) first introduced filter methods,which many authors lay emphysis on. In recent years, some research and progresses in this field have been made. Penalty-free method is a class of new algorithms, M.Ulbrich has investigated the case that the gradients of the constraints are linear independent. Being motivated mainly by this, our work generalizes and modifies the approach for linear denpendent assumption on the gradients of the constraints. We analyse a class of penalty-free nonmonotone trust-region methods for nonlinear equality constrained optimization problems in this paper. Without the linear independent assumption on the gradients of the constraints, the algorithmic framework yields global convergence and allows nonmonotonicity independently for both the constraint violation and the value of the Lagrangian function. Finally, some numerical results show that the method presented here is effective.更多还原