An Adaptive Method For Constrained Optimization Least-Squares Problems

Nonlinear least squares problem is extensively used in experimentation, projects and so on. As an special case of constrained optimization problems, it has a lot of methods to solve for its special structure. And SQP, region trust and the quasi-Newton equation are often used in solving this problem.This paper describes a new trust-region algorithm for nonlinear constrained optimization problems, according to its especial properties and combining SQP and trust-region method. For avoiding complications of computing two the rank information items, we emphasized to update the reduced- Hessian matrix Z~T▽~2L(x,λ)Z = Z~TC(xk)Z + Z~TS(x_k,λ_k)Z of Lagrange function of least squares problem. We realize it by updating the rank information items Z~TS (x_k,λ_k)Z. We also discuss predicted function and the selection of the punish parameter and the radius of trust-region.At the end, we establish a global convergence theorem for this algorithm in some condition and numerical experiments are presented illustrating the rationality and validity of the algorithm.