This paper gives a method of descent for the locally Lipschitzian function. It is assumed that the generalized subgradient set of the differentiable point is a singleton point. We introduce an implementable algorithm ...This paper gives a method of descent for the locally Lipschitzian function. It is assumed that the generalized subgradient set of the differentiable point is a singleton point. We introduce an implementable algorithm which is globally convergent. Numerical examples show the implementation and efficiency of the algorithm .展开更多
Under the non-Lipschitzian condition, a small time large deviation principle of diffusion processes on Hilbert spaces is established. The operator theory and Gronwall inequality play an important role.
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
文摘This paper gives a method of descent for the locally Lipschitzian function. It is assumed that the generalized subgradient set of the differentiable point is a singleton point. We introduce an implementable algorithm which is globally convergent. Numerical examples show the implementation and efficiency of the algorithm .
基金Supported by the National Basic Research Program of China (973 Program,Grant No.2007CB814901)the National Natural Science Foundation of China (Grant No.10826098)+1 种基金the Natural Science Foundation of Anhui Province (Grant No.090416225)Anhui Natural Science Foundation of Universities (Grant No.KJ2010A037)
文摘Under the non-Lipschitzian condition, a small time large deviation principle of diffusion processes on Hilbert spaces is established. The operator theory and Gronwall inequality play an important role.
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
