Non-monotone Conic Trust Region Methods Research

In this paper,we study the non-monotone trust region methods based on the conic model for unconstrained optimization.We combine the line search method,the self-adaptive trust-region radius method and the non-monotone strategy with the trust region method respectively.Based on that,we propose three new non-monotone conic model trust-region methods,and prove the global convergence property of the algorithm.Firstly,a non-monotone conic model trust-region method with non-monotone line search strategy is proposed.The new method does not resolve the trust region subproblem after the failure of the test step.Instead,it uses the non-monotone Wolfe-Type line search technique to get the next iteration point,which effectively improves the operation efficiency.Secondly,we incorporate the efficient adaptive updating method with the non-monotone trust-region method in order to a new non-monotone adaptive conic model trust-region method.The application of non-monotone technology and self-adaptive updating method of trust-region radius makes the resolution of the trust region sub-problem be effectively relieved.Thirdly,we combine the non-monotone Armijo-Type line search with the adaptive trust region method.This method uses a step that satisfies certain conditions to calculate the next iteration point when the test step fails.Meanwhile,a more simple method is adopted to update the trust-region radius.The application of the new method has achieved a significant reduction in the complexity of the algorithm.Finally,we summarize the method proposed in this paper,and talk about the further extension and expansion of the subject.