Solution of Equality Constrained Quadratic Programming Problems Arising in211 Optimization

摘要

We consider the application of the conjugate gradient method to the solution of211u001elarge equality constrainted quadratic programs arising in nonlinear optimization. 211u001eThe approach is based on a reduced linear system and generates iterates in the 211u001enull space of the constraints. Instead of computing a basis for this null space, 211u001ewe chose to work directly with the matrix of constraint gradients, computing 211u001eprojections into the null space by either a normal equations or an augmented 211u001esystem approach. This can yield substantial economies in both line search and 211u001etrust region methods for large-scale optimization, but can also result in 211u001esignificant rounding errors. We propose iterative refinement techniques, as well 211u001eas an adaptive reformulation of the quadratic problem, that can greatly reduce 211u001ethese errors without incurring in high computational overhead. Numerical results 211u001eillustrating the efficiency of the proposed approaches are presented.