A trust region method for conic model to solve unconstrained optimization

A trust region method for conic models to solve unconstrained optimization problems is proposed. We analyze the trust region approach for conic models and present necessary and sufficient conditions for the solution of the associated trust region subproblems. A corresponding numerical algorithm is developed and has been tested for 19 standard test functions in unconstrained optimization. The numerical results show that this method is superior to some advanced methods in the current software libraries. Finally, we prove that the proposed method has global convergence and Q-superlinear convergence properties.