By using a modified BFGS formula,a BFGS-type trust region method with line search technique for unconstrained optimization problems is proposed.

This paper presents a new self-adaptive trust region method for system of nonlinear equations and proves the global convergence and convergence rate under mild conditions.

A combined algorithm based on trust region method and gradient method is proposed.

In the first part, two trust region algorithms for linearly constrained optimization problem are proposed 1)Combining quasi-Newton and trust region method for linearly equality constrained optimization is given , its global convergence and super-linear rate is proved.

Trust region algorithm is anot.

Considering the algorithms for the nonlinearly constrained optimization problems, it focuses on researching the sequential quadratic programming (SQP) and trust region algorithm, which have a lot of successful results.

To achieve high accuracy,three strategies are adopted:1) a number of line spread functions (LSF) on each edge are extracted;2) different edge information is used;3) the trust-region method is employed to obtain optimal estimation of blur parameter.

This paper presents an affine-scaling interior-point trust region method for solving nonlinear equations with simple bounds.