Please use this identifier to cite or link to this item: https://doi.org/10.1007/BF01581136
Title: A trust region algorithm for minimization of locally Lipschitzian functions
Authors: Qi, L.
Sun, J. 
Keywords: Global convergence
Locally Lipschitzian functions
Trust region methods
Issue Date: 1994
Source: Qi, L., Sun, J. (1994). A trust region algorithm for minimization of locally Lipschitzian functions. Mathematical Programming 66 (1-3) : 25-43. ScholarBank@NUS Repository. https://doi.org/10.1007/BF01581136
Abstract: The classical trust region algorithm for smooth nonlinear programs is extended to the nonsmooth case where the objective function is only locally Lipschitzian. At each iteration, an objective function that carries both first and second order information is minimized over a trust region. The term that carries the first order information is an iteration function that may not explicitly depend on subgradients or directional derivatives. We prove that the algorithm is globally convergent. This convergence result extends the result of Powell for minimization of smooth functions, the result of Yuan for minimization of composite convex functions, and the result of Dennis, Li and Tapia for minimization of regular functions. In addition, compared with the recent model of Pang, Han and Rangaraj for minimization of locally Lipschitzian functions using a line search, this algorithm has the same convergence property without assuming positive definiteness and uniform boundedness of the second order term. Applications of the algorithm to various nonsmooth optimization problems are discussed. © 1994 The Mathematical Programming Society, Inc.
Source Title: Mathematical Programming
URI: http://scholarbank.nus.edu.sg/handle/10635/44945
ISSN: 00255610
DOI: 10.1007/BF01581136
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