In this note, the following unconstrained nonsmooth optimization problem is considered where f(x):R^n→R is only a locally Lipschitzian function. Many papers appear on the convergence properties of the trust region al...In this note, the following unconstrained nonsmooth optimization problem is considered where f(x):R^n→R is only a locally Lipschitzian function. Many papers appear on the convergence properties of the trust region algorithm to solve several different particular nonsmooth problems. Dennis, Li and Tapia proposed a general trust region model by using regular functions. They proved the global convergence of the general trust region model under some mild conditions which are shown to be satisfied by many trust region algorithms including smooth one. Qi and Sun provided another trust region model展开更多
This paper presents an augmented Lagrangian algorithm for nonlinear opti- mization of equality and bounded constraints. The method includes internal it- erations and outer iterations, which uses a trust region interio...This paper presents an augmented Lagrangian algorithm for nonlinear opti- mization of equality and bounded constraints. The method includes internal it- erations and outer iterations, which uses a trust region interior-point method in internal iteration. Under some conditions, the paper proves finite termination of internal iteration and analyses the local convergence of accelerating internal mini- mizer iterations. It also proves the global convergence of main algorithm when the approximate solution of internal minimizer is satisfied some conditions.展开更多
文摘In this note, the following unconstrained nonsmooth optimization problem is considered where f(x):R^n→R is only a locally Lipschitzian function. Many papers appear on the convergence properties of the trust region algorithm to solve several different particular nonsmooth problems. Dennis, Li and Tapia proposed a general trust region model by using regular functions. They proved the global convergence of the general trust region model under some mild conditions which are shown to be satisfied by many trust region algorithms including smooth one. Qi and Sun provided another trust region model
文摘This paper presents an augmented Lagrangian algorithm for nonlinear opti- mization of equality and bounded constraints. The method includes internal it- erations and outer iterations, which uses a trust region interior-point method in internal iteration. Under some conditions, the paper proves finite termination of internal iteration and analyses the local convergence of accelerating internal mini- mizer iterations. It also proves the global convergence of main algorithm when the approximate solution of internal minimizer is satisfied some conditions.
