A self-adaptive conic filter-trust region method for unconstrained optimization and its global convergence

A conic filter-trust region algorithm is proposed for unconstrained optimization problems. The method can be regarded as a combination of filter technique and conic trust region method. When trail step is not accepted, we will use line search rules for a suitable step length, then generate next iterative point. It need not resolve the conic trust region subproblem. The theoretical analysis shows that the algorithm is not only global convergence but also super linearly convergence under some suitable conditions. Numerical results show that this algorithm is effective in minimizing unconstrained optimization problems.