求解一般半正定二次规划的数值稳定方法

Numerical stable methods for general positive semidefinite quadratic programming

针对非光滑优化中捆集算法之二次规划子问题数值求解的困难 ,详细研究了求解半正定二次规划问题的积极法 ,提出了一系列矩阵分解的存储方法和校正方法 ,较好地克服了半正定矩阵奇异性带来的数值求解的困难 ,在求解捆集算法的半正定二次规划子问题中取得了很好的效果 。

In order to solve the positive semidefinite quadratic programming problems arising from bundle methods for nonsmooth optimization, an algorithm based on Gill & Murry′s active set algorithm for positive semidefinite quadratic programming is given. The numerical techniques for modifying the matrix factorizations are studied in detail when a constraint is added or deleted, which can avoid the singularities of positive semidefinite matrix and keep the algorithm′s numerical stability. The corresponding numerical approach to compute the descent direction for positive semidefinite quadratic programming is also discussed. The improved algorithm can solve sub problems in bundle methods efficiently and has numerical stability.