Dennis, J.E. Jr.Li, Shou-BaiTapia, R.A.2018-06-182018-06-181989-07Dennis, J.E. Jr., Li, Shou-Bai and Tapia, R.A.. "A Unified Approach to Global Convergence of Trust Region Methods for Nonsmooth Optimization." (1989) <a href="https://hdl.handle.net/1911/101657">https://hdl.handle.net/1911/101657</a>.https://hdl.handle.net/1911/101657This paper investigates the global convergence of trust region (TR) methods for solving nonsmooth minimization problems. For a class of nonsmooth objective functions called regular functions, conditions are found on the TR local models that imply three fundamental convergence properties. These conditions are shown to be satisfied by Fletcher's TR method for solving constrained optimization problems, Powell for solving nonlinear fitting problems, Zhang, Kim & Lasdon's successive linear programming method for solving constrained problems, Duff, Nocedal & Reid's TR method for solving systems of nonlinear equations, and El Hallabi & Tapia's TR method for solving systems of nonlinear equations. Thus our results can be viewed as a unified convergence theory for TR methods for nonsmooth problems.41 ppengTechnical reportTR89-05