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

J. E. Dennis | Zendy; Shou-Bai B. Li | Zendy; R. A. Tapia | Zendy

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

Author(s) -

J. E. Dennis,

Shou-Bai B. Li,

R. A. Tapia

Publication year - 1995

Publication title -

mathematical programming

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.358

H-Index - 131

eISSN - 1436-4646

pISSN - 0025-5610

DOI - 10.1007/bf01585770

Subject(s) - mathematics , trust region , convergence (economics) , nonlinear programming , mathematical optimization , nonlinear system , local convergence , symbolic convergence theory , class (philosophy) , minification , optimization problem , iterative method , computer science , artificial intelligence , key (lock) , computer security , economics , radius , economic growth , physics , quantum mechanics

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 our results can be viewed as a unified convergence theory for TR methods for nonsmooth problems.

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