投影Hessian的内点回代算法解线性约束优化问题

提供非单调内点回代技术的信赖域投影Hessian算法解线性约束优化问题.基于矩阵QR分解的技巧,将仿射零空间的信赖域子问题变换成通常的信赖域子问题,然后结合线搜索技术,在每次迭代信赖域子问题都将产生新的回代内点.在合理的条件下,证明了算法不仅具有整体收敛性而且保持局部超线性收敛速率,引入非单调技术将克服病态问题,加速收敛性进程.

Projected Hessian Algorithm with Backtracking Interior Point Technique for Linear Constrained Optimization

We propose a new trust region projected Hessian algorithm with nonmonotonic backtracking interior point technique for linear constrained optimization. Based on performing QR decomposition of an affine scaling equality constraint matrix, the conducted subproblem in the algorithm is the general trust region subprob-lem defined by minimizing a quadratic function subject only to an ellipsoidal constraint. By using both trust region strategy and line search technique, each iterate switches to backtracking interior point step generated by the trust region subproblem. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion is used to speed up the convergence progress in some ill-conditioned cases.