A New Conic Model Trust Region Algorithm

In this dissertation, a new trust-region algorithm with conic model is researched, a discuss and supplement of the new trust-region algorithm with the conci model is proposed, primarily about solving the trust-region subproblem with the conic model. The convergence analysis and some numerical results are given at last to ensure the algorithm is feasible and efficient.First, a new trust-region algorithm with conic model which is proposed by Qin Ni is introduced. The theoretic foundation and the substance are presented after that. The algorithm determines the feasible region of the conic model by comparing wheather the distance between the centre of the trsut-region and the hyperplane and is more than the current trust-region radius or not. Trough the discuss and the analysis, we can find that the different select ofε0 can lead to the change of the relative position between the hyperplane and the trust-region. Hence the trust-region subproblem is translated into three different cases.Secondly, a detailed state and analysis aobut the sencod one of the three cases mentioned above is presented following. And the new thought of solving the trust-region subproblem with conic model is given out. The new trust-region algorithm with conic model based on that is constructed, the feasibility and the convergence are proved respectively. The convergent resluts show that the algorithm has global convergence.Finally, the algorithm program and the numerical test are performed. The results illustrate that the new trust-region alogrithm with conic model is feasible and efficient.