基于信赖域技术的处理带线性约束优化的内点算法

基于信赖域技术,本文提出了一个求解带线性等式和非负约束优化问题的内点算法,其特点是:为了求得搜索方向,算法在每一步迭代时仅需要求解一线性方程组系统,从而避免了求解带信赖域界的子问题,然后利用非精确的Armijo线搜索法来得到下一个迭代内点. 从数值计算的观点来看,这种技巧可减少计算量.在适当的条件下,文中还证明了该算法所产生的迭代序列的每一个聚点都是原问题的KKT点.

An Interior Point Algorithm for Linearly Constrained Programming Based on Trust Region Techniques

In this paper,an interior point algorithm based on the trust region techniques is proposed for solving nonlinear optimization problems with linear equality constraints and nonnegative variables.Unlike those existing trust-region-type interior point methods,this proposed method solves only a system of linear equations at each iteration,thus avoiding the need for solving a quadratic subproblem with a trust region bound,and then an inexact line search based on Armijo stepsize rule is used to compute the stepsize.From a computational point of view,this approach may reduce a computational effort.Under suitable conditions,it is proved that any accumulation of the sequence generated by the algorithm satisfies the first-order optimality condition.