A Reduced Preconditional Conjugate Gradient Path Method for LinearEquality Constrained Optimization
线性等式约束优化的既约预条件共轭梯度路径法

A reduced preconditional conjugate gradient path method with nonmonotonic technique for linear equality constrained optimization problem is proposed. By using the generalized elimination method, the subproblem is equivalent to an unconstrained optimization problem in the null space of constrained matrix. We develop preconditioners based on an extended system. By employing the reduced preconditional conjugate gradient path search strategy, we obtain an iterative direction by solving the quadratic model as well as the iterative step. Based on the good properties of the conjugate gradient path, the global convergence results of the proposed algorithm are proved while fast local superlinear convergence rate is established under some reasonable conditions. Furthermore, numerical results indicate that the algorithm is feasible and effective.