An Affine-scaling Interior-point Trust Region Method For Nonlinear Equations With Simple Bounds

An interior-point method introduced recently by J.B. Francisco,N. Krejic and J. M. Martinez for solving box-constrainedunderdetermined nonlinear systems. In this paper, we present anaffine-scaling interior-point trust region method for solving nonlinearequations with simple bounds. The new method uses the nonmonotonestructure which relaxes the conditions that the trial step is accepted. Sothe new method is more concise and more general.Firstly, we determine a trial step p_k by solving a trust-regionsub-problem. The projection will be used to maintain the feasibility ofthe trial point. Then the new step length will be shrunk to guarantee thatthe trial point will be interior point. When the sufficiently descentcondition isn't satisfied, the nonmonotone structure will be used todetermine whether the trial step is accepted. If the sufficiently descentcondition still isn't satisfied, then the radius of trust region will bedecreased. Under the standard assumptions, if the sequence {x_k}generated by this method doesn't terminate finitely, then every limitpoint of the sequence is stationary point of the problem.Finally, the numerical test report is given, which shows that thenew method is very effective.