| The constrained nonlinear least squares(CNLLS)problem has important appli-cations in scientific experiments,scientific computation,prediction,simulation,de-sign,and engineer.In this paper,we use the exact penalty method proposed by Coleman et al for CNLLS problem,which transforms the constrained the problem into the nons-mooth unconstrained problem by introducing penalty terms.The main contributions of this paper are as follows.First,we prove that any first order stationary point proposed by Coleman et al is equivalent to a Clarke stationary point in nonsmooth optimization.We construct twice continuously differentiable smoothing function of the exact penal-ty function,and the smoothing Newton-steepest descent algorithm.The smoothing Newton-steepest descent method algorithm combines the smoothing techniques with the Newton method that owns local superlinear convergence and the steepest descent method that has global convergence.We show that accumulation point of the sequence generated by the smoothing Newton-steepest descent method corresponding to the it-erates with strict decrease of the smoothing parameters is a Clarke stationary point.Numerical experiments on measurement regression problems and second-order least squares problems show that the smoothing Newton-steepest descent method via exact penalty can effectively solve constrained nonlinear least squares problems,Numerical performance is much better than the smoothing steepest descent method. |
