The Inexact Newton Method For Solving Equality Constrained Optimization Problem

We propse a valid algorithm fOr smooth equality constrained optintizatio11 prob-lem with n variables, The traditional Lagrange-Newton method is locally al1d q-quadratically convergellt ill [ ] aloue. Recently D. Cores And R.A. Tapia present anew algorithm that the augumented Lagrangian SQP-Newton method is locally all(lqquadratically convergent in x alone under a mild condition on the cl1oice of tl1epenalty pararneter and the choice of the Lagrange multipliers. we apply an algoritll111that is an optimal combination of an exact Newton step witl1 Choleski factorizatio1land several iIlexact Newton steps with preconditioned conjugate gradient subiteratiollsto the new algorithm.this valid algorithm is also precisely convergent with Q-order 2,but tlleoretically it8 average number of arithmetic operations per step is IIluch lcssthan corresponding number which Newton method needs fOr middle alld large scaleprobletns.