Action constrained quasi-Newton methods

摘要: At the heart of Newton based optimization methods is a sequence symmetric linear systems. Each consecutive system in this similar to next, so solving them separately waste computational eort. Here we describe automatic preconditioning techniques for iterative such sequences systems by maintaining an estimate inverse matrix. We update matrix with quasi-Newton type formulas on what call action constraint instead secant equation. implement estimated inverses as preconditioners Newton-CG method and prove quadratic termination. Our implementation rst parallel preconditioners, full limited memory variants. Tests logistic Support Vector Machine problems reveal that our very ecient, converging wall clock time before without preconditioning. Further tests set classic test robust. The makes these updates exible enough mesh trust-region active methods, exibility not present methods.