CAJ | 학술논문

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.
기우신뢰역기술,본문제출료일개구해대선성등식화비부약속우화문제적내점산법,기특점시:위료구득수색방향,산법재매일보질대시부수요구해일선성방정조계통,종이피면료구해대신뢰역계적자문제,연후이용비정학적Armijo선수색법래득도하일개질대내점.종수치계산적관점래간,저충기교가감소계산량.재괄당적조건하,문중환증명료해산법소산생적질대서렬적매일개취점도시원문제적KKT점.
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.