不等式约束优化一个基于滤子思想的广义梯度投影算法

讨论非线性不等式约束优化问题, 借鉴于滤子算法思想,提出了一个新型广义梯度投影算法.该方法既不使用罚函数又无真正意义下的滤子.每次迭代通过一个简单的显式广义投影法产生搜索方向,步长由目标函数值或者约束违反度函数值充分下降的Armijo型线搜索产生.算法的主要特点是: 不需要迭代序列的有界性假设;不需要传统滤子算法所必需的可行恢复阶段;使用了ε积极约束集减小计算量.在合适的假设条件下算法具有全局收敛性, 最后对算法进行了初步的数值实验.

A GENERALIZED GRADIENT PROJECTION METHOD BASED ON THE IDEA OF FILTER FOR INEQUALITY CONSTRAINED OPTIMIZATION

In this paper, optimization problems with nonlinear inequality constraints are discussed. Based on the idea of the filter algorithm, a new generalized gradient projection algorithm is proposed. The proposed method uses neither a penalty function, nor a strict filter. At each iteration of the proposed algorithm, the search direction is yield by just on explicit generalized gradient projection. The step-size is selected such that either the value of the objective function or the measure of the constraint violations is sufficiently reduced by a Armijo line search technique. The main properties of the proposed algorithm as follows: don’t need to assume the boundness of iteration sequence; don’t need any restoration phase which is necessary for filter methods; the scale and the computation cost are further decreased by using the ε-active set. The algorithm is globally convergent under suitable assumptions. Finally, some elementary numerical experiments are reported.