The Projected Levenberg-marquardt Methods For Bound Constrained Nonlinear Equations

We present two kinds of projected Levenberg-Marquardt(LM) algorithms forbox constrained nonlinear equations. One is based on the trust region strategy,the other is based on the line search strategy. The trust-region projected LMalgorithm combines the projected LM step with the trust region strategy. Thegeneralized Cauchy step is computed to guarantee the decrease of the measurefunction. Under some conditions, the algorithm converges globally and convergessuperlinearly with the order32under the local error bound condition. The linesearch projected LM algorithm combines the projected LM step with line searchstrategy. In this algorithm, we must make some revision to the projected LMstep. The algorithm also converges globally. Numerical results show that thesetwo projected LM algorithms are efcient.