A unified approach to global convergence of trust region methods for nonsmooth optimization

A unified approach to global convergence of trust region methods for nonsmooth optimization

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Article ID: iaor19971118
Country: Netherlands
Volume: 68
Issue: 3
Start Page Number: 319
End Page Number: 346
Publication Date: Mar 1995
Journal: Mathematical Programming (Series A)
Authors: , ,
Keywords: trust regions
Abstract:

This 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 appropriate forms of Fletcher’s TR method for solving constrained optimization problems, Powell and Yuan’s TR method for solving nonlinear fitting problems, Zhang, Kim and Lasdon’s successive linear programming method for solving constrained problems, Duff, Nocedal and Reid’s TR method for solving systems of nonlinear equations, and El Hallabi and Tapia’s TR method for solving systems of nonlinear equations. Thus the present results can be viewed as a unified convergence theory for TR methods for nonsmooth problems.

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